## Yor, Marc

Compute Distance To:
 Author ID: yor.marc Published as: Yor, Marc; Yor, M. External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef · theses.fr
 Documents Indexed: 469 Publications since 1973, including 20 Books 35 Contributions as Editor · 2 Further Contributions Biographic References: 7 Publications Co-Authors: 168 Co-Authors with 406 Joint Publications 3,876 Co-Co-Authors
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### Co-Authors

 97 single-authored 43 Pitman, Jim William 38 Azéma, Jacques 36 Roynette, Bernard 23 Donati-Martin, Catherine 20 Madan, Dilip B. 20 Vallois, Pierre 17 Émery, Michel 16 Hirsch, Francis 15 Geman, Hélyette 15 Matsumoto, Hiroyuki 15 Meyer, Paul-André 13 Jeulin, Thierry 12 Bertoin, Jean 11 Yen, Ju-Yi J. 10 Petit, Frédérique 9 Barlow, Martin T. 9 Carmona, Philippe 8 Biane, Philippe 8 Salminen, Paavo H. 8 Shi, Zhan 7 Ledoux, Michel 6 Chaumont, Loïc 6 Fujita, Takahiko 6 Hariya, Yuu 6 Jeanblanc, Monique 5 Carr, Peter P. 5 Hu, Yueyun 5 Le Gall, Jean-François 5 Nikeghbali, Ashkan 5 Peccati, Giovanni 5 Vakeroudis, Stavros 4 El Karoui, Nicole 4 Funaki, Tadahisa 4 Knight, Frank Bardsley 4 Revuz, Daniel 4 Rosenbaum, Mathieu 4 Shiryaev, Al’bert Nikolaevich 4 Song, Shiqi 4 Stroock, Daniel W. 4 Wu, Ching-Tang 4 Yano, Kouji 3 Bru, Bernard 3 Chesney, Marc 3 Eberlein, Ernst W. 3 Elworthy, K. David 3 Föllmer, Hans 3 Gallardo, Léonard 3 Jacka, Saul D. 3 Mansuy, Roger 3 Najnudel, Joseph 3 Pistorius, Martijn R. 3 Profeta, Christophe 3 Rouault, Alain 3 Stricker, Christophe 3 Yano, Yuko 3 Zani, Marguerite 2 Alili, Larbi 2 Bismut, Jean-Michel 2 Bourgade, Paul 2 Bruss, Franz Thomas 2 Burdzy, Krzysztof 2 Chassaing, Philippe 2 Dang Ngoc Nghiem 2 De Meyer, Bernard 2 Doeblin, Wolfgang 2 Doney, Ronald Arthur 2 Dubins, Lester E. 2 Dufresne, Daniel 2 Ewald, Christian-Oliver 2 Ghomrasni, Raouf 2 Gnedin, Alexander V. 2 Göing-Jaeschke, Anja 2 Gradinaru, Mihai 2 Gundy, Richard F. 2 Hughes, C. P. 2 Jacod, Jean 2 Kella, Offer 2 Kozlov, Sergeĭ Mikhaĭlovich 2 Lépingle, Dominique 2 Li, Xue-Mei 2 Marckert, Jean-François 2 Obloj, Jan K. 2 O’Connell, Neil 2 Pap, Gyula 2 Tsilevich, Natalia V. 2 Vares, Maria Eulalia 2 Vershik, Anatoliĭ Moiseevich 2 Warren, Jon 2 Weinryb, Sophie 2 Zambotti, Lorenzo 1 Atlan, Marc 1 Auerhan, J. 1 Balazard, Michel 1 Baldi, Paolo 1 Barrieu, Pauline M. 1 Bentkus, Vidmants-Kastytis 1 Berthelot, Pierre 1 Bickel, Peter John 1 Bony, Jean-Michel 1 Bouleau, Nicolas ...and 87 more Co-Authors
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### Serials

 33 Lecture Notes in Mathematics 16 Stochastic Processes and their Applications 14 Electronic Communications in Probability 13 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 12 The Annals of Probability 12 Studia Scientiarum Mathematicarum Hungarica 12 Probability Theory and Related Fields 12 Comptes Rendus de l’Académie des Sciences. Série I 12 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 10 Mathematical Finance 9 Bernoulli 8 Journal of Applied Probability 7 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 7 Statistics & Probability Letters 7 Electronic Journal of Probability 6 Probability Surveys 5 Advances in Applied Probability 5 Periodica Mathematica Hungarica 5 Theory of Probability and its Applications 5 Publications of the Research Institute for Mathematical Sciences, Kyoto University 5 Probability and Mathematical Statistics 5 Revista Matemática Iberoamericana 5 Finance and Stochastics 5 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 Journal of Functional Analysis 4 Journal of Theoretical Probability 4 The Annals of Applied Probability 4 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 4 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Grundlehren der Mathematischen Wissenschaften 4 Japanese Journal of Mathematics. 3rd Series 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Bulletin des Sciences Mathématiques. Deuxième Série 3 Gazette des Mathématiciens 3 Journal of Mathematics of Kyoto University 3 Journal of the Mathematical Society of Japan 3 Proceedings of the London Mathematical Society. Third Series 3 Quantitative Finance 3 Cambridge Series in Statistical and Probabilistic Mathematics 3 Springer Finance 2 Stochastics 2 Annales de l’Institut Fourier 2 Bulletin of the London Mathematical Society 2 Illinois Journal of Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Nagoya Mathematical Journal 2 Transactions of the American Mathematical Society 2 Insurance Mathematics & Economics 2 Publicacions Matemàtiques 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Stochastics and Stochastics Reports 2 Potential Analysis 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 Computational and Applied Mathematics 2 Applied Mathematical Finance 2 Methodology and Computing in Applied Probability 2 Annals of Finance 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Advances in Mathematics 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Osaka Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Ergodic Theory and Dynamical Systems 1 Journal of Economic Dynamics & Control 1 Journal of Physics A: Mathematical and General 1 Expositiones Mathematicae 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Mathematical Sciences (New York) 1 European Mathematical Society Newsletter 1 Markov Processes and Related Fields 1 Taiwanese Journal of Mathematics 1 International Journal of Theoretical and Applied Finance 1 Theory of Stochastic Processes 1 Asia-Pacific Financial Markets 1 Astérisque 1 Travaux en Cours 1 MSJ Memoirs 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Mathematics and Financial Economics 1 Journal of Physics A: Mathematical and Theoretical 1 Bocconi & Springer Series 1 Pacific Journal of Mathematics for Industry 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Le Sel et le Fer 1 Universitext
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### Fields

 474 Probability theory and stochastic processes (60-XX) 50 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 40 General and overarching topics; collections (00-XX) 19 History and biography (01-XX) 9 Special functions (33-XX) 9 Statistics (62-XX) 5 Number theory (11-XX) 5 Measure and integration (28-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Real functions (26-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 2 Systems theory; control (93-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Partial differential equations (35-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

403 Publications have been cited 8,395 times in 5,253 Documents Cited by Year
Continuous martingales and Brownian motion. 3rd ed. Zbl 0917.60006
Revuz, Daniel; Yor, Marc
1999
Continuous martingales and Brownian motion. Zbl 0731.60002
Revuz, Daniel; Yor, Marc
1991
Stochastic volatility for Lévy processes. Zbl 1092.91022
Carr, Peter; Geman, Hélyette; Madan, Dilip B.; Yor, Marc
2003
Mathematical methods for financial markets. Zbl 1205.91003
Jeanblanc, Monique; Yor, Marc; Chesney, Marc
2009
The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Zbl 0880.60076
Pitman, Jim; Yor, Marc
1997
Continuous martingales and Brownian motion. 2nd ed. Zbl 0804.60001
Revuz, Daniel; Yor, Marc
1994
Continuous martingales and Brownian motion. 3rd ed., 3rd. corrected printing. Zbl 1087.60040
Revuz, Daniel; Yor, Marc
2005
Bessel processes, Asian options, and perpetuities. Zbl 0884.90029
Geman, Hélyette; Yor, Marc
1993
On some exponential functionals of Brownian motion. Zbl 0765.60084
Yor, Marc
1992
A decomposition of Bessel bridges. Zbl 0484.60062
Pitman, Jim; Yor, Marc
1982
Exponential functionals of Brownian motion and related processes. Zbl 0999.60004
Yor, Marc
2001
A survey and some generalizations of Bessel processes. Zbl 1038.60079
Göing-Jaeschke, Anja; Yor, Marc
2003
Size-biased sampling of Poisson point processes and excursions. Zbl 0741.60037
Perman, Mihael; Pitman, Jim; Yor, Marc
1992
Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local times. Zbl 0505.60054
Barlow, M. T.; Yor, M.
1982
Brownian analogues of Burke’s theorem. Zbl 1058.60078
O’Connell, Neil; Yor, Marc
2001
Brownian excursions and Parisian barrier options. Zbl 0882.60042
Chesney, Marc; Jeanblanc-Picqué, Monique; Yor, Marc
1997
Changes of filtrations and of probability measures. Zbl 0415.60048
Bremaud, Pierre; Yor, Marc
1978
Exponential functionals of Lévy processes. Zbl 1189.60096
Bertoin, Jean; Yor, Marc
2005
On models of default risk. Zbl 1042.91038
Elliott, R. J.; Jeanblanc, M.; Yor, M.
2000
Exponential functionals of Brownian motion. I: Probability laws at fixed time. Zbl 1189.60150
Matsumoto, Hiroyuki; Yor, Marc
2005
Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Zbl 1040.11061
Biane, Philippe; Pitman, Jim; Yor, Marc
2001
On the distribution and asymptotic results for exponential functionals of Lévy processes. Zbl 0905.60056
Carmona, Philippe; Petit, Frédérique; Yor, Marc
1997
Some aspects of Brownian motion, Part I: Some special functionals. Zbl 0779.60070
Yor, Marc
1992
Pricing and hedging double-barrier options: A probabilistic approach. Zbl 0915.90016
Geman, Hélyette; Yor, Marc
1996
Calcul stochastique dépendant d’un paramètre. Zbl 0388.60056
Stricker, C.; Yor, M.
1978
Self-decomposability and option pricing. Zbl 1278.91157
Carr, Peter; Geman, Hélyette; Madan, Dilip B.; Yor, Marc
2007
Valeurs principales associées aux temps locaux Browniens. (Principal values associated to Brownian local times). Zbl 0619.60072
Biane, Ph.; Yor, M.
1987
Time changes for Lévy processes. Zbl 0983.60082
Geman, Hélyette; Madan, Dilip B.; Yor, Marc
2001
Equivalent and absolutely continuous measure changes for jump-diffusion processes. Zbl 1082.60034
Cheridito, Patrick; Filipović, Damir; Yor, Marc
2005
Markovian bridges: Construction, Palm interpretation, and splicing. Zbl 0844.60054
Fitzsimmons, Pat; Pitman, Jim; Yor, Marc
1992
Loi de l’indice du lacet Brownien, et distribution de Hartman-Watson. Zbl 0436.60057
Yor, Marc
1980
Bessel processes and infinitely divisible laws. Zbl 0469.60076
Pitman, Jim; Yor, Marc
1981
Random times and enlargements of filtrations in a Brownian setting. Zbl 1103.60003
Mansuy, Roger; Yor, Marc
2006
Some aspects of Brownian motion. Part II: Some recent martingale problems. Zbl 0880.60082
Yor, Marc
1997
Making Markov martingales meet marginals: With explicit constructions. Zbl 1009.60037
2002
Pricing options on realized variance. Zbl 1096.91022
Carr, Peter; Geman, Hélyette; Madan, Dilip B.; Yor, Marc
2005
Grossissement d’une filtration et semi-martingales: formules explicites. Zbl 0411.60045
Jeulin, T.; Yor, M.
1978
Asymptotic laws of planar Brownian motion. Zbl 0607.60070
Pitman, Jim; Yor, Marc
1986
Exponential functionals of Brownian motion. II: Some related diffusion processes. Zbl 1189.91232
Matsumoto, Hiroyuki; Yor, Marc
2005
On Walsh’s Brownian motions. Zbl 0747.60072
Barlow, Martin; Pitman, Jim; Yor, Marc
1989
On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Zbl 1024.60030
Bertoin, Jean; Yor, Marc
2001
Peacocks and associated martingales, with explicit constructions. Zbl 1227.60001
Hirsch, Francis; Profeta, Christophe; Roynette, Bernard; Yor, Marc
2011
A multi- dimensional extension of the arcsine law. (Une extension multidimensionnelle de la loi de l’arc sinus.) Zbl 0738.60072
Barlow, Martin; Pitman, Jim; Yor, Marc
1989
The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1004.60046
Bertoin, Jean; Yor, Marc
2002
Arcsine laws and interval partitions derived from a stable subordinator. Zbl 0769.60014
Pitman, Jim; Yor, Marc
1992
Une solution simple au problème de Skorokhod. Zbl 0414.60055
Azema, Jacques; Yor, Marc
1979
Beta-gamma random variables and intertwining relations between certain Markov processes. Zbl 0919.60074
Carmona, Philippe; Petit, Frédérique; Yor, Marc
1998
The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes. Zbl 0960.60046
Elworthy, K. D.; Li, Xue-Mei; Yor, M.
1999
An analogue of Pitman’s $$2M-X$$ theorem for exponential Winer functionals. II: The role of the generalized inverse Gaussian laws. Zbl 0983.60075
Matsumoto, Hiroyuki; Yor, Marc
2001
Infinitely divisible laws associated with hyperbolic functions. Zbl 1039.11054
Pitman, Jim; Yor, Marc
2003
Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples. Zbl 1189.60035
James, Lancelot F.; Roynette, Bernard; Yor, Marc
2008
An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. Zbl 0990.60053
Tsilevich, Natalia; Vershik, Anatoly; Yor, Marc
2001
On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1031.60038
Bertoin, Jean; Yor, Marc
2002
Exercises in probability. A guided tour from measure theory to random processes, via conditioning. Zbl 1065.60001
Chaumont, L.; Yor, M.
2003
Grossissements de filtrations: exemples et applications. Séminaire de Calcul Stochastique 1982/83, Université Paris VI. Zbl 0547.00034
1985
Exponential functionals of Brownian motion and disordered systems. Zbl 0929.60063
Comtet, Alain; Monthus, Cécile; Yor, Marc
1998
Aspects of Brownian motion. Zbl 1162.60022
Mansuy, Roger; Yor, Marc
2008
A representation for non-colliding random walks. Zbl 1037.15019
O’Connell, Neil; Yor, Marc
2002
On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options. Zbl 0979.60073
Donati-Martin, Catherine; Ghomrasni, Raouf; Yor, Marc
2001
Étude des solutions extremales et représentation intégrale des solutions pour certains problèmes de martingales. Zbl 0346.60032
Jacod, Jean; Yor, Marc
1977
Sur la variation quadratique des temps locaux de certaines semimartingales. Zbl 0476.60046
Bouleau, Nicolas; Yor, Marc
1981
Asymptotic laws for compositions derived from transformed subordinators. Zbl 1142.60327
Gnedin, Alexander; Pitman, Jim; Yor, Marc
2006
(Semi-) martingale inequalities and local times. Zbl 0451.60050
Barlow, M. T.; Yor, M.
1981
Hitting, occupation and inverse local times of one-dimensional diffusions: Martingale and excursion approaches. Zbl 1024.60032
Pitman, Jim; Yor, Marc
2003
Exponential functionals of Lévy processes. Zbl 0979.60038
Carmona, Philippe; Petit, Frédérique; Yor, Marc
2001
Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws. Zbl 1076.60067
Donati-Martin, Catherine; Doumerc, Yan; Matsumoto, Hiroyuki; Yor, Marc
2004
An analogue of Pitman’s $$2M-X$$ theorem for exponential Wiener functionals. I: A time-inversion approach. Zbl 0963.60076
Matsumoto, Hiroyuki; Yor, Marc
2000
On quadratic functionals of the Brownian sheet and related processes. Zbl 1090.60020
Deheuvels, Paul; Peccati, Giovanni; Yor, Marc
2006
Some penalisations of the Wiener measure. Zbl 1160.60315
Roynette, B.; Vallois, P.; Yor, M.
2006
Existence et unicité de diffusions à valeurs dans un espace de Hilbert. Zbl 0281.60094
Yor, M.
1974
Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. Zbl 0877.60053
Pitman, Jim; Yor, Marc
1996
Fubini’s theorem for double Wiener integrals and the variance of the Brownian path. Zbl 0738.60074
Donati-Martin, C.; Yor, M.
1991
On certain exponential functionals of the real Bownian motion. (Sur certaines fonctionnelles exponentielles du mouvement brownien réel.) Zbl 0758.60085
Yor, Marc
1992
Doob’s maximal identity, multiplicative decompositions and enlargements of filtrations. Zbl 1101.60059
Nikeghbali, Ashkan; Yor, Marc
2006
Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time, II. Zbl 1121.60004
Roynette, Bernard; Vallois, Pierre; Yor, Marc
2006
A definition and some characteristic properties of pseudo-stopping times. Zbl 1083.60035
Nikeghbali, Ashkan; Yor, Marc
2005
On the excursion theory for linear diffusions. Zbl 1160.60024
Salminen, Paavo; Vallois, Pierre; Yor, Marc
2007
Les inégalités des sous-martingales, comme consequences de la rélation de domination. Zbl 0437.60038
Yor, Marc
1979
On the exponential functionals of certain Lévy processes. (Sur les fonctionnelles exponentielles de certains processus de Lévy.) Zbl 0830.60072
Carmona, P.; Petit, F.; Yor, M.
1994
The characteristic polynomial of a random unitary matrix: a probabilistic approach. Zbl 1155.15025
Bourgade, P.; Hughes, C. P.; Nikeghbali, A.; Yor, M.
2008
On D. Williams’ ”pinching method” and some applications. Zbl 0518.60088
Messulam, P.; Yor, M.
1982
Renormalisation et convergence en loi pour les temps locaux d’intersection du mouvement brownien dans $${\mathbb{R}}^ 3$$. Zbl 0569.60075
Yor, M.
1985
The Brownian burglar: Conditioning Brownian motion by its local time process. Zbl 0924.60072
Warren, J.; Yor, M.
1998
Further asymptotic laws of planar Brownian motion. Zbl 0686.60085
Pitman, Jim; Yor, Marc
1989
Some martingales associated to reflected Lévy processes. Zbl 1079.60048
Nguyen-Ngoc, Laurent; Yor, Marc
2005
Some new examples of Markov processes which enjoy the time-inversion property. Zbl 1087.60058
Gallardo, Léonard; Yor, Marc
2005
Harnesses, Lévy bridges and Monsieur Jourdain. Zbl 1070.60041
Mansuy, Roger; Yor, Marc
2005
Self-similar processes with independent increments associated with Lévy and Bessel processes. Zbl 1059.60052
Jeanblanc, M.; Pitman, Jim; Yor, Marc
2002
A study of the Hartman-Watson distribution motivated by numerical problems related to the pricing of Asian options. Zbl 1064.60021
Barrieu, P.; Rouault, A.; Yor, M.
2004
Ito’s integrated formula for strict local martingales. Zbl 1133.60025
2006
A clarification note about hitting times densities for Ornstein-Uhlenbeck processes. Zbl 1064.60026
Göing-Jaeschke, Anja; Yor, Marc
2003
Stochastic time changes in catastrophe option pricing. Zbl 0894.90046
Geman, Helyette; Yor, Marc
1997
Exponential functionals and principal values related to Brownian motion. A collection of research papers. Zbl 0889.00015
1997
A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration. Zbl 0981.60078
Matsumoto, Hiroyuki; Yor, Marc
2001
On probability characteristics of “downfalls” in a standard Brownian motion. Zbl 0959.60073
Douady, R.; Shiryaev, A. N.; Yor, M.
1999
Inégalité de Hardy, semimartingales, et faux-amis. Zbl 0419.60049
Jeulin, T.; Yor, M.
1979
On a theorem of Tsirelson with respect to Brownian and non-Brownian filtrations. (Autour d’un théorème de Tsirelson sur des filtrations browniennes et non browniennes.) Zbl 0914.60064
Barlow, M. T.; Émery, M.; Knight, F. B.; Song, S.; Yor, M.
1998
Asymptotic laws for regenerative compositions: gamma subordinators and the like. Zbl 1099.60023
Gnedin, Alexander; Pitman, Jim; Yor, Marc
2006
Option prices as probabilities. A new look at generalized Black-Scholes formulae. Zbl 1188.91004
Profeta, Christophe; Roynette, Bernard; Yor, Marc
2010
On Bougerol’s inequality for exponential functions of Brownian motions. (Sur l’identité de Bougerol pour les fonctionnelles exponentielles du mouvement brownien avec drift.) Zbl 0905.60059
Alili, Larbi; Dufresne, Daniel; Yor, Marc
1997
On peacocks and lyrebirds: Australian options, Brownian bridges, and the average of submartingales. Zbl 1390.91299
Ewald, Christian-Oliver; Yor, Marc
2018
Unifying the Dynkin and Lebesgue-Stieltjes formulae. Zbl 1400.60059
Kella, Offer; Yor, Marc
2017
On valuing stochastic perpetuities using new long horizon stock price models distinguishing booms, busts, and balanced markets. Zbl 1348.91272
2016
Kellerer’s theorem revisited. Zbl 1368.60045
Hirsch, Francis; Roynette, Bernard; Yor, Marc
2015
Around Tsirelson’s equation, or: the evolution process may not explain everything. Zbl 1328.60170
Yano, Kouji; Yor, Marc
2015
Some explicit formulas for the Brownian bridge, Brownian meander and Bessel process under uniform sampling. Zbl 1333.60181
Rosenbaum, Mathieu; Yor, Marc
2015
Integral representations of certain measures in the one-dimensional diffusions excursion theory. Zbl 1334.60165
Salminen, Paavo; Yen, Ju-Yi; Yor, Marc
2015
Random scaling and sampling of Brownian motion. Zbl 1335.60157
Rosenbaum, Mathieu; Yor, Marc
2015
A Gaussian martingale which is the sum of two independent Gaussian non-semimartingales. Zbl 1329.60099
Yor, Marc
2015
On increasing risk, inequality and poverty measures: peacocks, lyrebirds and exotic options. Zbl 1401.91135
Ewald, Christian-Oliver; Yor, Marc
2015
Bid and ask prices as non-linear continuous time G-expectations based on distortions. Zbl 1307.91086
Eberlein, Ernst; Madan, Dilip B.; Pistorius, Martijn; Yor, Marc
2014
Two price economies in continuous time. Zbl 1298.91086
Eberlein, Ernst; Madan, Dilip; Pistorius, Martijn; Schoutens, Wim; Yor, Marc
2014
How to make Dupire’s local volatility work with jumps. Zbl 1402.91776
Friz, Peter K.; Gerhold, Stefan; Yor, Marc
2014
On the expectation of normalized Brownian functionals up to first hitting times. Zbl 1291.60164
Elie, Romuald; Rosenbaum, Mathieu; Yor, Marc
2014
On the law of a triplet associated with the pseudo-Brownian bridge. Zbl 1390.60298
Rosenbaum, Mathieu; Yor, Marc
2014
Local times for functions with finite variation: two versions of Stieltjes change-of-variables formula. Zbl 1295.26011
Bertoin, Jean; Yor, Marc
2014
On the one-sided maximum of Brownian and random walk fragments and its applications to new exotic options called “meander option”. Zbl 1386.91140
Fujita, Takahiko; Kawanishi, Yasuhiro; Yor, Marc
2014
Comparing Brownian stochastic integrals for the convex order. Zbl 1322.60079
Hirsch, Francis; Yor, Marc
2014
Local times and excursion theory for Brownian motion. A tale of Wiener and Itô measures. Zbl 1364.60003
Yen, Ju-Yi; Yor, Marc
2013
On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator. Zbl 1287.60096
Hirsch, Francis; Yor, Marc
2013
Integrability properties and limit theorems for the exit time from a cone of planar Brownian motion. Zbl 1294.60103
Vakeroudis, Stavros; Yor, Marc
2013
Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Zbl 1303.60073
Bertoin, Jean; Dufresne, Daniel; Yor, Marc
2013
On the remarkable Lamperti representation of the inverse local time of a radial Ornstein-Uhlenbeck process. Zbl 1287.60048
Hirsch, Francis; Yor, Marc
2013
Some examples of Skorokhod embeddings obtained from the Azéma-Yor algorithm. Zbl 1258.60032
Lim, Adrian P. C.; Yen, Ju-Yi; Yor, Marc
2013
A simple stochastic rate model for rate equity hybrid products. Zbl 1396.91780
Eberlein, Ernst; Madan, Dilip; Pistorius, Martijn; Yor, Marc
2013
Retrieving information from subordination. Zbl 1284.60084
Bertoin, Jean; Yor, Marc
2013
Pure jump increasing processes and the change of variables formula. Zbl 1306.60120
Bertoin, Jean; Yor, Marc
2013
On an identity in law between Brownian quadratic functionals. Zbl 1290.60081
Yen, Ju-Yi; Yor, Marc
2013
Exercises in probability. A guided tour from measure theory to random processes via conditioning. 2nd ed. Zbl 1246.60001
Chaumont, Loïc; Yor, Marc
2012
Some infinite divisibility properties of the reciprocal of planar Brownian motion exit time from a cone. Zbl 1259.60097
Vakeroudis, Stavros; Yor, Marc
2012
On temporally completely monotone functions for Markov processes. Zbl 1245.60071
Hirsch, Francis; Yor, Marc
2012
Stochastic processes with proportional increments and the last-arrival problem. Zbl 1255.60166
Bruss, F. Thomas; Yor, Marc
2012
A scaling proof for Walsh’s Brownian motion extended arc-sine law. Zbl 1323.60115
Vakeroudis, Stavros; Yor, Marc
2012
A central limit theorem for a sequence of Brownian motions in the unit sphere in $$\mathbb R^{n}$$. Zbl 1239.60022
Vakeroudis, S.; Yor, M.
2012
Stochastic filtering at Saint-Flour. Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 876 (1981) and 1464 (1991). Zbl 1397.60010
El Karoui, Nicole; Pardoux, Etienne; Yor, Marc
2012
Moments of Wiener integrals for subordinators. Zbl 1329.60165
2012
Peacocks and associated martingales, with explicit constructions. Zbl 1227.60001
Hirsch, Francis; Profeta, Christophe; Roynette, Bernard; Yor, Marc
2011
The mean first rotation time of a planar polymer. Zbl 1221.82159
Vakeroudis, S.; Yor, M.; Holcman, D.
2011
On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes. Zbl 1274.60251
Salminen, Paavo; Yor, Marc
2011
The S&P 500 index as a Sato process travelling at the speed of the VIX. Zbl 1239.91186
2011
Call option prices based on Bessel processes. Zbl 1217.60071
Yen, Ju-Yi; Yor, Marc
2011
Constructing self-similar martingales via two Skorokhod embeddings. Zbl 1234.60047
Hirsch, Francis; Profeta, Christophe; Roynette, Bernard; Yor, Marc
2011
A sequence of Albin type continuous martingales with Brownian marginals and scaling. Zbl 1216.60039
Baker, David; Donati-Martin, Catherine; Yor, Marc
2011
From an Itô type calculus for Gaussian processes to integrals of log-normal processes increasing in the convex order. Zbl 1233.60008
Hirsch, Francis; Roynette, Bernard; Yor, Marc
2011
Options on realized variance and convex orders. Zbl 1277.91164
Carr, Peter; Geman, Helyette; Madan, Dilip B.; Yor, Marc
2011
Option prices as probabilities. A new look at generalized Black-Scholes formulae. Zbl 1188.91004
Profeta, Christophe; Roynette, Bernard; Yor, Marc
2010
Penalisation of a stable Lévy process involving its one-sided supremum. Zbl 1208.60046
Yano, Kouji; Yano, Yuko; Yor, Marc
2010
Looking for martingales associated to a self-decomposable law. Zbl 1225.60131
Hirsch, Francis; Yor, Marc
2010
Unifying constructions of martingales associated with processes increasing in the convex order, via Lévy and Sato sheets. Zbl 1223.60027
Hirsch, Francis; Roynette, Bernard; Yor, Marc
2010
A new formula for some linear stochastic equations with applications. Zbl 1196.60122
Kella, Offer; Yor, Marc
2010
Applying Itō’s motto: “Look at the infinite dimensional picture” by constructing sheets to obtain processes increasing in the convex order. Zbl 1274.60052
Hirsch, Francis; Roynette, Bernard; Yor, Marc
2010
A tribute to Professor Kiyosi Itô. Zbl 1178.01066
Yor, M.; Vares, M. E.; Mikosch, T.
2010
Mathematical methods for financial markets. Zbl 1205.91003
Jeanblanc, Monique; Yor, Marc; Chesney, Marc
2009
Penalising Brownian paths. Dedicated to Frank Knight (1933-2007). Zbl 1190.60002
Roynette, Bernard; Yor, Marc
2009
On the laws of first hitting times of points for one-dimensional symmetric stable Lévy processes. Zbl 1201.60043
Yano, Kouji; Yano, Yuko; Yor, Marc
2009
A global view of Brownian penalisations. Zbl 1180.60004
Najnudel, J.; Roynette, B.; Yor, M.
2009
Penalising symmetric stable Lévy paths. Zbl 1180.60008
Yano, Kouji; Yano, Yuko; Yor, Marc
2009
A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion. Zbl 1201.60033
Baker, David; Yor, Marc
2009
The Barnes G function and its relations with sums and products of generalized gamma convolution variables. Zbl 1189.60073
Nikeghbali, Ashkan; Yor, Marc
2009
A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet. Zbl 1191.60040
Hirsch, Francis; Yor, Marc
2009
Exercises in probability. A guided tour from measure theory to random processes, via conditioning. Reprint of the 2003 hardback ed. Zbl 1180.60002
Chaumont, L.; Yor, M.
2009
A construction of processes with one dimensional martingale marginals, based upon path-space Ornstein-Uhlenbeck processes and the Brownian sheet. Zbl 1203.60122
Hirsch, Francis; Yor, Marc
2009
Penalisations of multidimensional Brownian motion. VI. Zbl 1189.60069
Roynette, Bernard; Vallois, Pierre; Yor, Marc
2009
Brownian penalisations related to excursion lengths. VII. Zbl 1181.60046
Roynette, B.; Vallois, P.; Yor, M.
2009
Fractional intertwinings between two Markov semigroups. Zbl 1175.26010
Hirsch, F.; Yor, M.
2009
Put option prices as joint distribution functions in strike and maturity: the Black-Scholes case. Zbl 1183.91179
Madan, Dilip B.; Roynette, Bernard; Yor, Marc
2009
A family of generalized gamma convoluted variables. Zbl 1197.60012
Roynette, B.; Vallois, P.; Yor, M.
2009
Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples. Zbl 1189.60035
James, Lancelot F.; Roynette, Bernard; Yor, Marc
2008
Aspects of Brownian motion. Zbl 1162.60022
Mansuy, Roger; Yor, Marc
2008
The characteristic polynomial of a random unitary matrix: a probabilistic approach. Zbl 1155.15025
Bourgade, P.; Hughes, C. P.; Nikeghbali, A.; Yor, M.
2008
On constants related to the choice of the local time at $$0$$, and the corresponding Itô measure for Bessel processes with dimension $$d=2(1-\alpha), 0<\alpha<1$$. Zbl 1212.60070
Donati-Martin, Catherine; Roynette, Bernard; Vallois, Pierre; Yor, Marc
2008
On the time to reach maximum for a variety of constrained Brownian motions. Zbl 1195.82020
Majumdar, Satya N.; Randon-Furling, Julien; Kearney, Michael J.; Yor, Marc
2008
Unifying Black-Scholes type formulae which involve Brownian last passage times up to a finite horizon. Zbl 1163.91414
Madan, Dilip B.; Roynette, Bernard; Yor, Marc
2008
An arithmetic model for the total disorder process. Zbl 1144.60020
Hughes, C. P.; Nikeghbali, A.; Yor, M.
2008
Harmonic and stochastic analysis of Dunkl processes. Zbl 1205.60005
2008
Quasi-invariance properties of a class of subordinators. Zbl 1180.60044
von Renesse, Max-K.; Yor, Marc; Zambotti, Lorenzo
2008
Penalizing a $$BES(d)$$ process $$(0<d<2)$$ with a function of its local time. V. Zbl 1164.60307
Roynette, Bernard; Vallois, Pierre; Yor, Marc
2008
Renewal series and square-root boundaries for Bessel processes. Zbl 1190.60031
Enriquez, Nathanael; Sabot, Christophe; Yor, Marc
2008
Penalisations of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding. Zbl 1224.60076
Roynette, B.; Vallois, P.; Yor, M.
2008
Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times. VIII. Zbl 1180.60070
Roynette, B.; Yor, M.
2008
Self-decomposability and option pricing. Zbl 1278.91157
Carr, Peter; Geman, Hélyette; Madan, Dilip B.; Yor, Marc
2007
On the excursion theory for linear diffusions. Zbl 1160.60024
Salminen, Paavo; Vallois, Pierre; Yor, Marc
2007
Tanaka formula for symmetric Lévy processes. Zbl 1129.60043
Salminen, Paavo; Yor, Marc
2007
Euler’s formulae for $$\zeta(2n)$$ and products of Cauchy variables. Zbl 1129.60088
Bourgade, Paul; Fujita, Takahiko; Yor, Marc
2007
Itô’s excursion theory and its applications. Zbl 1156.60066
Pitman, Jim; Yor, Marc
2007
Some remarkable properties of gamma processes. Zbl 1156.60030
Yor, Marc
2007
On the remarkable distributions of maxima of some fragments of the standard reflecting random walk and Brownian motion. Zbl 1130.60051
Fujita, Takahiko; Yor, Marc
2007
Further examples of explicit Krein representations of certain subordinators. Zbl 1129.60042
Donati-Martin, Catherine; Yor, Marc
2007
A remarkable $$\sigma$$-finite measure on $$\mathcal C(\mathbb{R}_+,\mathbb{R})$$ related to many Brownian penalisations. Zbl 1221.60003
Najnudel, Joseph; Roynette, Bernard; Yor, Marc
2007
Correlation and the pricing of risks. Zbl 1233.91320
Atlan, Marc; Geman, Hélyette; Madan, Dilip B.; Yor, Marc
2007
Some extensions of Pitman and Ray-Knight theorems for penalized Brownian motions and their local times, IV. Zbl 1164.60355
Roynette, Bernard; Vallois, Pierre; Yor, Marc
2007
On the problem of stochastic integral representations of functionals of the Brownian motion. II. Zbl 1116.60022
Graversen, S.; Shiryaev, A. N.; Yor, M.
2007
Probing option prices for information. Zbl 1157.60067
Geman, Hélyette; Madan, Dilip B.; Yor, Marc
2007
Wiener integrals for centered powers of Bessel processes. I. Zbl 1123.60035
Funaki, T.; Hariya, Y.; Yor, M.
2007
Some aspects of the probabilistic work. Zbl 1369.60003
Chaumont, Loïc; Mazliak, Laurent; Yor, Marc
2007
On some Fourier aspects of the construction of certain Wiener integrals. Zbl 1113.60055
Funaki, T.; Hariya, Y.; Hirsch, F.; Yor, M.
2007
A note about Selberg’s integrals in relation with the beta-gamma algebra. Zbl 1160.33002
Yor, Marc
2007
Random times and enlargements of filtrations in a Brownian setting. Zbl 1103.60003
Mansuy, Roger; Yor, Marc
2006
Asymptotic laws for compositions derived from transformed subordinators. Zbl 1142.60327
Gnedin, Alexander; Pitman, Jim; Yor, Marc
2006
On quadratic functionals of the Brownian sheet and related processes. Zbl 1090.60020
Deheuvels, Paul; Peccati, Giovanni; Yor, Marc
2006
...and 303 more Documents
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### Cited by 4,848 Authors

 121 Yor, Marc 48 Madan, Dilip B. 39 Jeanblanc, Monique 36 Pitman, Jim William 29 Vallois, Pierre 26 Le Gall, Jean-François 24 Ouknine, Youssef 24 Russo, Francesco 23 Nualart, David 23 Patie, Pierre 23 Shi, Zhan 22 Bertoin, Jean 21 Kyprianou, Andreas E. 21 Nikeghbali, Ashkan 21 Roynette, Bernard 20 Imkeller, Peter 20 Pardo, Juan Carlos 19 Ankirchner, Stefan 19 Favaro, Stefano 19 Hobson, David Graham 19 Iksanov, Aleksander M. 19 Khoshnevisan, Davar 19 Peccati, Giovanni 19 Yan, Litan 19 Yano, Kouji 18 Albeverio, Sergio A. 18 Gapeev, Pavel V. 18 Röckner, Michael 18 Schoutens, Wim 18 Zambotti, Lorenzo 17 Corwin, Ivan Z. 17 Hairer, Martin 17 Najnudel, Joseph 17 O’Connell, Neil 17 Peskir, Goran 17 Sheffield, Scott 16 Carr, Peter P. 16 Dalang, Robert C. 16 Ferrari, Giorgio 16 Palmowski, Zbigniew 16 Pardoux, Etienne 16 Protter, Philip Elliott 16 Prünster, Igor 16 Rutkowski, Marek 16 Simon, Thomas 16 Werner, Wendelin 16 Wiśniewolski, Maciej 15 Barczy, Mátyás 15 Cui, Zhenyu 15 Jakubowski, Jacek 15 Janson, Svante 15 Karatzas, Ioannis 15 Mijatović, Aleksandar 15 Pal, Soumik 15 Platen, Eckhard 15 Touzi, Nizar 15 Wesołowski, Jacek 15 Winkel, Matthias 14 El Karoui, Nicole 14 Flandoli, Franco 14 James, Lancelot F. 14 Kardaras, Constantinos 14 Obloj, Jan K. 14 Pistorius, Martijn R. 14 Schachermayer, Walter 13 Beiglböck, Mathias 13 Gnedin, Alexander V. 13 Gobet, Emmanuel 13 Lijoi, Antonio 13 Linetsky, Vadim 13 Matsumoto, Hiroyuki 13 Pap, Gyula 13 Privault, Nicolas 13 Rivero, Víctor Manuel 13 Siu, Tak Kuen 13 Zhou, Xiaowen 12 Borodin, Alexei 12 Dassios, Angelos 12 Döring, Leif 12 Eberlein, Ernst W. 12 Engelbert, Hans Jürgen 12 Fontana, Claudio 12 Forde, Martin 12 Hamadene, Saïd 12 Hu, Yueyun 12 Huillet, Thierry E. 12 Jacquier, Antoine 12 Katori, Makoto 12 Majumdar, Satya N. 12 Miller, Jason P. 12 Urusov, Mikhail A. 12 Wang, Guojing 12 Wu, Rong 12 Zhang, Xicheng 11 Bass, Richard F. 11 Baudoin, Fabrice 11 Bayraktar, Erhan 11 Çetin, Umut 11 Chaumont, Loïc 11 Chen, Zhen-Qing ...and 4,748 more Authors
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### Cited in 457 Serials

 458 Stochastic Processes and their Applications 256 The Annals of Probability 192 Probability Theory and Related Fields 179 The Annals of Applied Probability 168 Statistics & Probability Letters 136 Journal of Theoretical Probability 113 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 113 International Journal of Theoretical and Applied Finance 109 Bernoulli 109 Finance and Stochastics 107 Journal of Applied Probability 101 Journal of Statistical Physics 100 Quantitative Finance 86 Mathematical Finance 84 Insurance Mathematics & Economics 83 Stochastic Analysis and Applications 76 Journal of Mathematical Analysis and Applications 71 Electronic Journal of Probability 69 Journal of Functional Analysis 65 Advances in Applied Probability 54 Potential Analysis 51 Transactions of the American Mathematical Society 51 Stochastics 49 Applied Mathematical Finance 47 Communications in Mathematical Physics 44 SIAM Journal on Financial Mathematics 40 Journal of Computational and Applied Mathematics 36 Journal of Econometrics 33 Comptes Rendus. Mathématique. Académie des Sciences, Paris 32 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 32 Methodology and Computing in Applied Probability 31 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 31 Mathematics and Financial Economics 30 Proceedings of the American Mathematical Society 30 Electronic Communications in Probability 30 Annals of Finance 26 The Annals of Statistics 26 Applied Mathematics and Optimization 25 SIAM Journal on Control and Optimization 25 Bulletin des Sciences Mathématiques 25 ALEA. Latin American Journal of Probability and Mathematical Statistics 24 Journal of Economic Dynamics & Control 24 Stochastics and Dynamics 23 Journal of Multivariate Analysis 22 Journal of Mathematical Physics 22 Theory of Probability and its Applications 21 Review of Derivatives Research 20 Applied Mathematics and Computation 20 Asia-Pacific Financial Markets 20 Electronic Journal of Statistics 19 European Journal of Operational Research 18 Communications in Statistics. Theory and Methods 18 Probability Surveys 17 Journal of Differential Equations 17 Science China. Mathematics 16 Journal of Statistical Planning and Inference 16 Journal of Mathematical Sciences (New York) 16 Stochastic Models 16 Stochastic and Partial Differential Equations. Analysis and Computations 15 Stochastics 15 Econometric Theory 14 Queueing Systems 14 Statistical Inference for Stochastic Processes 14 Decisions in Economics and Finance 14 Journal of Statistical Mechanics: Theory and Experiment 14 Bayesian Analysis 13 Frontiers of Mathematics in China 12 Lithuanian Mathematical Journal 12 Advances in Mathematics 12 Acta Applicandae Mathematicae 12 Annals of Operations Research 12 Stochastics and Stochastics Reports 12 Abstract and Applied Analysis 12 Statistics and Computing 11 Physica A 11 Publications of the Research Institute for Mathematical Sciences, Kyoto University 11 Probability and Mathematical Statistics 11 Acta Mathematicae Applicatae Sinica. English Series 11 Statistical Science 11 Journal of Applied Mathematics and Stochastic Analysis 11 Infinite Dimensional Analysis, Quantum Probability and Related Topics 11 Annales Henri Poincaré 11 Modern Stochastics. Theory and Applications 10 Computers & Mathematics with Applications 10 Communications on Pure and Applied Mathematics 10 Annales de l’Institut Fourier 10 Annals of the Institute of Statistical Mathematics 10 Duke Mathematical Journal 10 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 10 Scandinavian Actuarial Journal 10 North American Actuarial Journal 9 Journal of Mathematical Biology 9 Scandinavian Journal of Statistics 9 Inventiones Mathematicae 9 Journal of Economic Theory 9 Computational Statistics and Data Analysis 9 Theory of Probability and Mathematical Statistics 9 ASTIN Bulletin 8 Journal of the Mathematical Society of Japan ...and 357 more Serials
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### Cited in 58 Fields

 4,266 Probability theory and stochastic processes (60-XX) 1,503 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 668 Statistics (62-XX) 410 Partial differential equations (35-XX) 321 Statistical mechanics, structure of matter (82-XX) 264 Numerical analysis (65-XX) 232 Systems theory; control (93-XX) 133 Biology and other natural sciences (92-XX) 116 Global analysis, analysis on manifolds (58-XX) 115 Calculus of variations and optimal control; optimization (49-XX) 109 Operator theory (47-XX) 98 Combinatorics (05-XX) 95 Ordinary differential equations (34-XX) 95 Operations research, mathematical programming (90-XX) 90 Dynamical systems and ergodic theory (37-XX) 79 Special functions (33-XX) 68 Potential theory (31-XX) 67 Measure and integration (28-XX) 63 Functional analysis (46-XX) 62 Quantum theory (81-XX) 61 Linear and multilinear algebra; matrix theory (15-XX) 60 Number theory (11-XX) 54 Integral transforms, operational calculus (44-XX) 41 Fluid mechanics (76-XX) 38 Real functions (26-XX) 37 Harmonic analysis on Euclidean spaces (42-XX) 37 Integral equations (45-XX) 34 Functions of a complex variable (30-XX) 32 Differential geometry (53-XX) 32 Computer science (68-XX) 28 Topological groups, Lie groups (22-XX) 24 Approximations and expansions (41-XX) 21 Abstract harmonic analysis (43-XX) 14 Information and communication theory, circuits (94-XX) 13 History and biography (01-XX) 11 Convex and discrete geometry (52-XX) 9 Several complex variables and analytic spaces (32-XX) 9 Geophysics (86-XX) 8 Nonassociative rings and algebras (17-XX) 8 Group theory and generalizations (20-XX) 8 Mechanics of particles and systems (70-XX) 7 Mechanics of deformable solids (74-XX) 6 Mathematical logic and foundations (03-XX) 6 Relativity and gravitational theory (83-XX) 5 Sequences, series, summability (40-XX) 5 Manifolds and cell complexes (57-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Algebraic geometry (14-XX) 4 Difference and functional equations (39-XX) 4 General topology (54-XX) 2 General and overarching topics; collections (00-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Mathematics education (97-XX) 1 Associative rings and algebras (16-XX) 1 $$K$$-theory (19-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX)

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