## Lyons, Terence John

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 Author ID: lyons.terence-j Published as: Lyons, Terry; Lyons, T. J.; Lyons, Terry J.; Lyons, T.; Lyons, Terence J. more...less External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 108 Publications since 1980, including 2 Books 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 55 Co-Authors with 77 Joint Publications 1,408 Co-Co-Authors
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### Co-Authors

 23 single-authored 8 Crisan, Dan O. 8 Qian, Zhongmin M. 6 Litterer, Christian 6 Yang, Danyu 5 Zhang, Tusheng S. 4 Cass, Thomas Richard 4 Hambly, Ben M. 3 Gyurkó, Lajos Gergely 3 Ni, Hao 3 Perez Arribas, Imanol 3 Xu, Weijun 3 Zheng, Weian 2 Boedihardjo, Horatio 2 Chang, Jiawei 2 Del Moral, Pierre 2 Friz, Peter Karl 2 Gaines, J. G. 2 Hara, Keisuke 2 Hayman, Walter Kurt 2 Nejad, Sina 2 Röckner, Michael 2 Stoica, Lucreţiu 2 Victoir, Nicolas B. 1 Albeverio, Sergio A. 1 Barnett, Chris 1 Bass, Richard F. 1 Beliaev, Dmitri B. 1 Boutaib, Youness 1 Caruana, Michael 1 Chevyrev, Ilya 1 Duplantier, Bertrand 1 Eremenko, Alexandre Émmanuilovich 1 Flint, Guy H. 1 Gaines, Jessica 1 Gamelin, Theodore W. 1 Gassiat, Paul 1 Geng, Xi 1 Kalsi, Jasdeep 1 Kershaw, Donald 1 Lawler, Gregory Francis 1 Le Gall, Jean-François 1 Ledoux, Michel 1 Lee, Wonjung 1 Lejay, Antoine 1 Levin, Daniel 1 Lévy, Thierry 1 Li, Xiang-Dong 1 Liang, Gechun 1 Lunt, John 1 MacGibbon, Brenda 1 Margarint, Vlad 1 McKean, Henry P. jun. 1 Oberhauser, Harald 1 Reuter, G. E. H. 1 Rozanov, Yuriĭ Anatol’evich 1 Salisbury, Thomas S. 1 Salvi, Cristopher 1 Sidorova, Nadia 1 Stroock, Daniel W. 1 Sullivan, Dennis Parnell 1 Taylor, John C. 1 Yam, Phillip S. C. 1 Yang, Weixin 1 Zeitouni, Ofer
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### Serials

 10 The Annals of Probability 9 Journal of Functional Analysis 6 Bulletin of the London Mathematical Society 5 Probability Theory and Related Fields 3 Journal of Differential Geometry 3 Revista Matemática Iberoamericana 3 SIAM Journal on Applied Mathematics 3 Applied Mathematical Finance 2 Advances in Applied Probability 2 Advances in Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Stochastic Processes and their Applications 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Electronic Communications in Probability 2 Journal of the European Mathematical Society (JEMS) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Illinois Journal of Mathematics 1 Journal of the Mathematical Society of Japan 1 Mathematische Annalen 1 Proceedings of the London Mathematical Society. Third Series 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 The Annals of Applied Probability 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Stochastics and Stochastics Reports 1 Mathematical Research Letters 1 Bulletin des Sciences Mathématiques 1 Monte Carlo Methods and Applications 1 Sbornik: Mathematics 1 Markov Processes and Related Fields 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Communications in Mathematical Sciences 1 Fields Institute Communications 1 Lecture Notes in Mathematics 1 Publications in Sciences. University of Joensuu 1 SIAM Journal on Financial Mathematics 1 Oxford Mathematical Monographs 1 SIAM Journal on Mathematics of Data Science
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### Fields

 82 Probability theory and stochastic processes (60-XX) 19 Potential theory (31-XX) 19 Systems theory; control (93-XX) 16 Numerical analysis (65-XX) 13 Ordinary differential equations (34-XX) 13 Global analysis, analysis on manifolds (58-XX) 8 Functions of a complex variable (30-XX) 8 Functional analysis (46-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Partial differential equations (35-XX) 4 Real functions (26-XX) 4 Differential geometry (53-XX) 2 Measure and integration (28-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Abstract harmonic analysis (43-XX) 2 Operator theory (47-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

96 Publications have been cited 1,892 times in 992 Documents Cited by Year
Differential equations driven by rough signals. Zbl 0923.34056
Lyons, Terry J.
1998
System control and rough paths. Zbl 1029.93001
Lyons, Terry; Qian, Zhongmin
2002
Differential equations driven by rough signals. I: An extension of an inequality of L. C. Young. Zbl 0835.34004
Lyons, Terry
1994
Differential equations driven by rough paths. Ecole d’Eté de Probabilités de Saint-Flour XXXIV – 2004. Lectures given at the 34th probability summer school, July 6–24, 2004. Zbl 1176.60002
Lyons, Terry J.; Caruana, Michael; Lévy, Thierry
2007
Cubature on Wiener space. Zbl 1055.60049
Lyons, Terry; Victoir, Nicolas
2004
Function theory, random paths and covering spaces. Zbl 0554.58022
Lyons, Terry; Sullivan, Dennis
1984
Variable step size control in the numerical solution of stochastic differential equations. Zbl 0888.60046
Gaines, J. G.; Lyons, T. J.
1997
A simple criterion for transience of a reversible Markov chain. Zbl 0509.60067
Lyons, Terry
1983
Integrability and tail estimates for Gaussian rough differential equations. Zbl 1278.60091
Cass, Thomas; Litterer, Christian; Lyons, Terry
2013
Decomposition of Dirichlet processes and its applications. Zbl 0804.60044
Lyons, T. J.; Zhang, T. S.
1994
Uniqueness for the signature of a path of bounded variation and the reduced path group. Zbl 1276.58012
Hambly, Ben; Lyons, Terry
2010
Random generation of stochastic area integrals. Zbl 0805.60052
Gaines, J. G.; Lyons, T. J.
1994
An extension theorem to rough paths. Zbl 1134.60047
Lyons, Terry; Victoir, Nicolas
2007
Nonlinear filtering and measure-valued processes. Zbl 0888.93056
Crisan, Dan; Lyons, Terry
1997
A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Zbl 0654.60059
Lyons, Terence J.; Zheng, Weian
1988
Integrability of functionals of Dirichlet processes, probabilistic representations of semigroups, and estimates of heat kernels. Zbl 0914.60045
Lunt, John; Lyons, T. J.; Zhang, T. S.
1998
Lévy area of Wiener processes in Banach spaces. Zbl 1016.60071
Ledoux, M.; Lyons, T.; Qian, Z.
2002
On conditional diffusion processes. Zbl 0715.60097
Lyons, T. J.; Zheng, W. A.
1990
Discrete filtering using branching and interacting particle systems. Zbl 0967.93088
Crisan, D.; Del Moral, P.; Lyons, T.
1999
Winding of the plane Brownian motion. Zbl 0541.60075
Lyons, T. J.; McKean, H. P.
1984
Convergence of a branching particle method to the solution of the Zakai equation. Zbl 0915.93060
Crisan, Dan; Gaines, Jessica; Lyons, Terry
1998
Finely holomorphic functions. Zbl 0459.46038
Lyons, T. J.
1980
A particle approximation of the solution of the Kushner-Stratonovitch equation. Zbl 0951.93068
Crisan, D.; Lyons, T.
1999
Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains. Zbl 0599.60011
Lyons, Terry
1987
Efficient and practical implementations of cubature on Wiener space. Zbl 1221.65009
Gyurkó, Lajos Gergely; Lyons, Terry J.
2011
Extending the Wong-Zakai theorem to reversible Markov processes. Zbl 1010.60070
Bass, R. F.; Hambly, B. M.; Lyons, T. J.
2002
Physical Brownian motion in a magnetic field as a rough path. Zbl 1390.60257
Friz, Peter; Gassiat, Paul; Lyons, Terry
2015
Stochastic area for Brownian motion on the Sierpiński gasket. Zbl 0936.60073
Hambly, B. M.; Lyons, T. J.
1998
High order recombination and an application to cubature on Wiener space. Zbl 1261.65011
Litterer, Christian; Lyons, Terence J.
2012
The signature of a rough path: uniqueness. Zbl 1347.60094
Boedihardjo, Horatio; Geng, Xi; Lyons, Terry; Yang, Danyu
2016
The limits of stochastic integrals of differential forms. Zbl 0969.60078
Lyons, Terry; Stoica, Lucreţiu
1999
Characteristic functions of measures on geometric rough paths. Zbl 1393.60008
Chevyrev, Ilya; Lyons, Terry
2016
Backward stochastic dynamics on a filtered probability space. Zbl 1238.60064
Liang, Gechun; Lyons, Terry; Qian, Zhongmin
2011
Flow of diffeomorphisms induced by a geometric multiplicative functional. Zbl 0918.60009
Lyons, Terry; Qian, Zhongmin
1998
Rough paths, signatures and the modelling of functions on streams. Zbl 1373.93158
Lyons, Terry
2014
Minimal entropy approximations and optimal algorithms. Zbl 1018.65014
Crisan, Dan; Lyons, Terry
2002
Evolving communities with individual preferences. Zbl 1321.60204
Cass, Thomas; Lyons, Terry
2015
On the non-existence of path integrals. Zbl 0745.60051
Lyons, Terry
1991
Smoothness of Itô maps and diffusion processes on path spaces. I. Zbl 1127.60033
Li, Xiang-Dong; Lyons, Terry J.
2006
Lévy’s area under conditioning. Zbl 1099.60054
Friz, P.; Lyons, T.; Stroock, D.
2006
Bases for positive continuous functions. Zbl 0675.30040
Hayman, W. K.; Lyons, T. J.
1990
On the importance of the Lévy area for studying the limits of functions of converging stochastic processes. Application to homogenization. Zbl 1199.60292
Lejay, Antoine; Lyons, Terry
2005
The critical dimension at which quasi-every Brownian path is self- avoiding. Zbl 0609.60087
Lyons, Terry J.
1986
Discretely sampled signals and the rough Hoff process. Zbl 1348.60058
Flint, Guy; Hambly, Ben; Lyons, Terry
2016
A note on tightness of capacities associated with Dirichlet forms. Zbl 0781.60063
Lyons, Terry; Röckner, Michael
1992
Flow equations on spaces of rough paths. Zbl 0890.58090
Lyons, Terry; Qian, Zhongmin
1997
A class of vector fields on path spaces. Zbl 0877.58059
Lyons, T. J.; Qian, Z. M.
1997
Stopping non-commutative processes. Zbl 0585.60058
Barnett, Chris; Lyons, Terry
1986
Convergence of non-symmetric Dirichlet processes. Zbl 0888.31005
Lyons, Terry; Zhang, Tusheng
1996
System control and rough paths. Zbl 1044.93009
Lyons, T. J.
2002
Inverting the signature of a path. Zbl 1429.70012
Lyons, Terry J.; Xu, Weijun
2018
Stochastic Jacobi fields and vector fields induced by varying area on path spaces. Zbl 0903.60008
Lyons, Terry; Qian, Zhongmin
1997
Hyperbolic development and inversion of signature. Zbl 1362.53009
Lyons, Terry J.; Xu, Weijun
2017
A signed measure on rough paths associated to a PDE of high order: results and conjectures. Zbl 1193.60071
Levin, Daniel; Lyons, Terry
2009
Instability of the conservative property under quasi-isometries. Zbl 0747.53034
Lyons, Terry
1991
Dimension-free Euler estimates of rough differential equations. Zbl 1399.60115
Boutaib, Youness; Gyurkó, Lajos Gergely; Lyons, Terry; Yang, Danyu
2014
Interacting particle systems approximations of the Kushner-Stratonovitch equation. Zbl 0947.60040
Crişan, D.; Del Moral, P.; Lyons, T. J.
1999
A synthetic proof of Makarov’s law of the iterated logarithm. Zbl 0708.30033
Lyons, Terry
1990
Diffusion processes with non-smooth diffusion coefficients and their density functions. Zbl 0715.60096
Lyons, T. J.; Zheng, W. A.
1990
Random thoughts on reversible potential theory. Zbl 0757.31007
Lyons, Terry
1992
The geometry of the Brownian curve. Zbl 0778.60058
Duplantier, B.; Lawler, G. F.; Le Gall, J.-F.; Lyons, T. J.
1993
Uncertain volatility and the risk-free synthesis of derivatives. Zbl 1466.91347
Lyons, T. J.
1995
Rough paths based numerical algorithms in computational finance. Zbl 1198.91229
Gyurkó, Lajos Gergely; Lyons, Terry
2010
The interpretation and solution of ordinary differential equations driven by rough signals. Zbl 0827.34049
Lyons, Terry J.
1995
Note on convergence of Dirichlet processes. Zbl 0793.31006
Lyons, T. J.; Zhang, T. S.
1993
On the radius of convergence of the logarithmic signature. Zbl 1103.60060
2006
The best harmonic approximant to a continuous function. Zbl 0541.41024
Hayman, Walter K.; Kershaw, Donald; Lyons, Terry J.
1984
A theorem in fine potential theory and applications to finely holomorphic functions. Zbl 0459.46039
Lyons, T. J.
1980
Cones of lower semicontinuous functions and a characterisation of finely hyperharmonic functions. Zbl 0492.31005
Lyons, Terry J.
1982
Conditional exponential moments for iterated Wiener integrals. Zbl 0961.60053
Lyons, Terry; Zeitouni, Ofer
1999
Systems controlled by rough paths. Zbl 1125.93026
Lyons, Terry
2005
Calculus for multiplicative functionals, Itô’s formula and differential equations. Zbl 0862.60043
Lyons, T. J.; Qian, Z. M.
1996
On Gauss-Green theorem and boundaries of a class of Hölder domains. Zbl 1103.28007
Lyons, Terry J.; Yam, Phillip S. C.
2006
Projection theorems for hitting probabilities and a theorem of Littlewood. Zbl 0566.58036
Lyons, T. J.; MacGibbon, K. B.; Taylor, J. C.
1984
Expected signature of Brownian motion up to the first exit time from a bounded domain. Zbl 1350.60086
Lyons, Terry; Ni, Hao
2015
Kusuoka-Stroock gradient bounds for the solution of the filtering equation. Zbl 1333.60147
Crisan, Dan; Litterer, Christian; Lyons, Terry
2015
Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length. (Supermultiplicativité et une borne inférieure pour la décroissance de la signature d’un chemin de longueur finie.) Zbl 1391.60163
Chang, Jiawei; Lyons, Terry; Ni, Hao
2018
The adaptive patched cubature filter and its implementation. Zbl 1343.60042
Lee, Wonjung; Lyons, Terry
2016
Rough paths on manifolds. Zbl 1280.58023
Cass, Thomas; Litterer, Christian; Lyons, Terry
2012
Introducing cubature to filtering. Zbl 1237.93168
Litterer, C.; Lyons, T.
2011
Cubature on Wiener space continued. Zbl 1187.35299
Litterer, Christian; Lyons, Terry
2007
Jensen measures for R(K). Zbl 0509.31002
Gamelin, T. W.; Lyons, T. J.
1983
Finely harmonic functions need not be quasi-analytic. Zbl 0541.31002
Lyons, Terry
1984
Uniform factorial decay estimates for controlled differential equations. Zbl 1333.60117
Boedihardjo, Horatio; Lyons, Terry; Yang, Danyu
2015
Numerical method for model-free pricing of exotic derivatives in discrete time using rough path signatures. Zbl 1437.91431
Lyons, Terry; Nejad, Sina; Perez Arribas, Imanol
2019
An optimal polynomial approximation of Brownian motion. Zbl 1434.60226
Foster, James; Lyons, Terry; Oberhauser, Harald
2020
Optimal execution with rough path signatures. Zbl 1443.91263
Kalsi, Jasdeep; Lyons, Terry; Arribas, Imanol Perez
2020
Recovering the pathwise Itô solution from averaged Stratonovich solutions. Zbl 1338.60148
Lyons, Terry; Yang, Danyu
2016
A uniform estimate for rough paths. Zbl 1296.60155
Lyons, Terry J.; Xu, Weijun
2013
Kiyoshi Itô (1915–2008). Zbl 1201.60005
Lyons, Terence J.
2010
The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example – an improvement of Menshov-Rademacher theorem. Zbl 1284.42082
Lyons, Terry J.; Yang, Danyu
2013
Smooth rough paths and applications to Fourier analysis. Zbl 1146.26004
Hara, Keisuke; Lyons, Terry
2007
On the limit of stochastic integrals of differential forms. Zbl 0899.60046
Lyons, Terry; Stoica, Lucreţiu
1996
On boundary conditions for stochastic evolution equations with an extremally chaotic source. Zbl 0869.60054
Albeverio, S.; Lyons, T.; Rozanov, Yu.
1995
Continuity in $$\kappa$$ in $$\mathrm{SLE}_\kappa$$ theory using a constructive method and rough path theory. Zbl 07374667
Beliaev, Dmitry; Lyons, Terry J.; Margarint, Vlad
2021
Corrigendum to: “Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length”. Zbl 1400.60089
Chang, Jiawei; Lyons, Terry; Ni, Hao
2018
Continuity in $$\kappa$$ in $$\mathrm{SLE}_\kappa$$ theory using a constructive method and rough path theory. Zbl 07374667
Beliaev, Dmitry; Lyons, Terry J.; Margarint, Vlad
2021
An optimal polynomial approximation of Brownian motion. Zbl 1434.60226
Foster, James; Lyons, Terry; Oberhauser, Harald
2020
Optimal execution with rough path signatures. Zbl 1443.91263
Kalsi, Jasdeep; Lyons, Terry; Arribas, Imanol Perez
2020
Numerical method for model-free pricing of exotic derivatives in discrete time using rough path signatures. Zbl 1437.91431
Lyons, Terry; Nejad, Sina; Perez Arribas, Imanol
2019
Inverting the signature of a path. Zbl 1429.70012
Lyons, Terry J.; Xu, Weijun
2018
Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length. (Supermultiplicativité et une borne inférieure pour la décroissance de la signature d’un chemin de longueur finie.) Zbl 1391.60163
Chang, Jiawei; Lyons, Terry; Ni, Hao
2018
Corrigendum to: “Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length”. Zbl 1400.60089
Chang, Jiawei; Lyons, Terry; Ni, Hao
2018
Hyperbolic development and inversion of signature. Zbl 1362.53009
Lyons, Terry J.; Xu, Weijun
2017
The signature of a rough path: uniqueness. Zbl 1347.60094
Boedihardjo, Horatio; Geng, Xi; Lyons, Terry; Yang, Danyu
2016
Characteristic functions of measures on geometric rough paths. Zbl 1393.60008
Chevyrev, Ilya; Lyons, Terry
2016
Discretely sampled signals and the rough Hoff process. Zbl 1348.60058
Flint, Guy; Hambly, Ben; Lyons, Terry
2016
The adaptive patched cubature filter and its implementation. Zbl 1343.60042
Lee, Wonjung; Lyons, Terry
2016
Recovering the pathwise Itô solution from averaged Stratonovich solutions. Zbl 1338.60148
Lyons, Terry; Yang, Danyu
2016
Physical Brownian motion in a magnetic field as a rough path. Zbl 1390.60257
Friz, Peter; Gassiat, Paul; Lyons, Terry
2015
Evolving communities with individual preferences. Zbl 1321.60204
Cass, Thomas; Lyons, Terry
2015
Expected signature of Brownian motion up to the first exit time from a bounded domain. Zbl 1350.60086
Lyons, Terry; Ni, Hao
2015
Kusuoka-Stroock gradient bounds for the solution of the filtering equation. Zbl 1333.60147
Crisan, Dan; Litterer, Christian; Lyons, Terry
2015
Uniform factorial decay estimates for controlled differential equations. Zbl 1333.60117
Boedihardjo, Horatio; Lyons, Terry; Yang, Danyu
2015
Rough paths, signatures and the modelling of functions on streams. Zbl 1373.93158
Lyons, Terry
2014
Dimension-free Euler estimates of rough differential equations. Zbl 1399.60115
Boutaib, Youness; Gyurkó, Lajos Gergely; Lyons, Terry; Yang, Danyu
2014
Integrability and tail estimates for Gaussian rough differential equations. Zbl 1278.60091
Cass, Thomas; Litterer, Christian; Lyons, Terry
2013
A uniform estimate for rough paths. Zbl 1296.60155
Lyons, Terry J.; Xu, Weijun
2013
The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example – an improvement of Menshov-Rademacher theorem. Zbl 1284.42082
Lyons, Terry J.; Yang, Danyu
2013
High order recombination and an application to cubature on Wiener space. Zbl 1261.65011
Litterer, Christian; Lyons, Terence J.
2012
Rough paths on manifolds. Zbl 1280.58023
Cass, Thomas; Litterer, Christian; Lyons, Terry
2012
Efficient and practical implementations of cubature on Wiener space. Zbl 1221.65009
Gyurkó, Lajos Gergely; Lyons, Terry J.
2011
Backward stochastic dynamics on a filtered probability space. Zbl 1238.60064
Liang, Gechun; Lyons, Terry; Qian, Zhongmin
2011
Introducing cubature to filtering. Zbl 1237.93168
Litterer, C.; Lyons, T.
2011
Uniqueness for the signature of a path of bounded variation and the reduced path group. Zbl 1276.58012
Hambly, Ben; Lyons, Terry
2010
Rough paths based numerical algorithms in computational finance. Zbl 1198.91229
Gyurkó, Lajos Gergely; Lyons, Terry
2010
Kiyoshi Itô (1915–2008). Zbl 1201.60005
Lyons, Terence J.
2010
A signed measure on rough paths associated to a PDE of high order: results and conjectures. Zbl 1193.60071
Levin, Daniel; Lyons, Terry
2009
Differential equations driven by rough paths. Ecole d’Eté de Probabilités de Saint-Flour XXXIV – 2004. Lectures given at the 34th probability summer school, July 6–24, 2004. Zbl 1176.60002
Lyons, Terry J.; Caruana, Michael; Lévy, Thierry
2007
An extension theorem to rough paths. Zbl 1134.60047
Lyons, Terry; Victoir, Nicolas
2007
Cubature on Wiener space continued. Zbl 1187.35299
Litterer, Christian; Lyons, Terry
2007
Smooth rough paths and applications to Fourier analysis. Zbl 1146.26004
Hara, Keisuke; Lyons, Terry
2007
Smoothness of Itô maps and diffusion processes on path spaces. I. Zbl 1127.60033
Li, Xiang-Dong; Lyons, Terry J.
2006
Lévy’s area under conditioning. Zbl 1099.60054
Friz, P.; Lyons, T.; Stroock, D.
2006
On the radius of convergence of the logarithmic signature. Zbl 1103.60060
2006
On Gauss-Green theorem and boundaries of a class of Hölder domains. Zbl 1103.28007
Lyons, Terry J.; Yam, Phillip S. C.
2006
On the importance of the Lévy area for studying the limits of functions of converging stochastic processes. Application to homogenization. Zbl 1199.60292
Lejay, Antoine; Lyons, Terry
2005
Systems controlled by rough paths. Zbl 1125.93026
Lyons, Terry
2005
Cubature on Wiener space. Zbl 1055.60049
Lyons, Terry; Victoir, Nicolas
2004
System control and rough paths. Zbl 1029.93001
Lyons, Terry; Qian, Zhongmin
2002
Lévy area of Wiener processes in Banach spaces. Zbl 1016.60071
Ledoux, M.; Lyons, T.; Qian, Z.
2002
Extending the Wong-Zakai theorem to reversible Markov processes. Zbl 1010.60070
Bass, R. F.; Hambly, B. M.; Lyons, T. J.
2002
Minimal entropy approximations and optimal algorithms. Zbl 1018.65014
Crisan, Dan; Lyons, Terry
2002
System control and rough paths. Zbl 1044.93009
Lyons, T. J.
2002
Discrete filtering using branching and interacting particle systems. Zbl 0967.93088
Crisan, D.; Del Moral, P.; Lyons, T.
1999
A particle approximation of the solution of the Kushner-Stratonovitch equation. Zbl 0951.93068
Crisan, D.; Lyons, T.
1999
The limits of stochastic integrals of differential forms. Zbl 0969.60078
Lyons, Terry; Stoica, Lucreţiu
1999
Interacting particle systems approximations of the Kushner-Stratonovitch equation. Zbl 0947.60040
Crişan, D.; Del Moral, P.; Lyons, T. J.
1999
Conditional exponential moments for iterated Wiener integrals. Zbl 0961.60053
Lyons, Terry; Zeitouni, Ofer
1999
Differential equations driven by rough signals. Zbl 0923.34056
Lyons, Terry J.
1998
Integrability of functionals of Dirichlet processes, probabilistic representations of semigroups, and estimates of heat kernels. Zbl 0914.60045
Lunt, John; Lyons, T. J.; Zhang, T. S.
1998
Convergence of a branching particle method to the solution of the Zakai equation. Zbl 0915.93060
Crisan, Dan; Gaines, Jessica; Lyons, Terry
1998
Stochastic area for Brownian motion on the Sierpiński gasket. Zbl 0936.60073
Hambly, B. M.; Lyons, T. J.
1998
Flow of diffeomorphisms induced by a geometric multiplicative functional. Zbl 0918.60009
Lyons, Terry; Qian, Zhongmin
1998
Variable step size control in the numerical solution of stochastic differential equations. Zbl 0888.60046
Gaines, J. G.; Lyons, T. J.
1997
Nonlinear filtering and measure-valued processes. Zbl 0888.93056
Crisan, Dan; Lyons, Terry
1997
Flow equations on spaces of rough paths. Zbl 0890.58090
Lyons, Terry; Qian, Zhongmin
1997
A class of vector fields on path spaces. Zbl 0877.58059
Lyons, T. J.; Qian, Z. M.
1997
Stochastic Jacobi fields and vector fields induced by varying area on path spaces. Zbl 0903.60008
Lyons, Terry; Qian, Zhongmin
1997
Convergence of non-symmetric Dirichlet processes. Zbl 0888.31005
Lyons, Terry; Zhang, Tusheng
1996
Calculus for multiplicative functionals, Itô’s formula and differential equations. Zbl 0862.60043
Lyons, T. J.; Qian, Z. M.
1996
On the limit of stochastic integrals of differential forms. Zbl 0899.60046
Lyons, Terry; Stoica, Lucreţiu
1996
Uncertain volatility and the risk-free synthesis of derivatives. Zbl 1466.91347
Lyons, T. J.
1995
The interpretation and solution of ordinary differential equations driven by rough signals. Zbl 0827.34049
Lyons, Terry J.
1995
On boundary conditions for stochastic evolution equations with an extremally chaotic source. Zbl 0869.60054
Albeverio, S.; Lyons, T.; Rozanov, Yu.
1995
Differential equations driven by rough signals. I: An extension of an inequality of L. C. Young. Zbl 0835.34004
Lyons, Terry
1994
Decomposition of Dirichlet processes and its applications. Zbl 0804.60044
Lyons, T. J.; Zhang, T. S.
1994
Random generation of stochastic area integrals. Zbl 0805.60052
Gaines, J. G.; Lyons, T. J.
1994
The geometry of the Brownian curve. Zbl 0778.60058
Duplantier, B.; Lawler, G. F.; Le Gall, J.-F.; Lyons, T. J.
1993
Note on convergence of Dirichlet processes. Zbl 0793.31006
Lyons, T. J.; Zhang, T. S.
1993
A note on tightness of capacities associated with Dirichlet forms. Zbl 0781.60063
Lyons, Terry; Röckner, Michael
1992
Random thoughts on reversible potential theory. Zbl 0757.31007
Lyons, Terry
1992
On the non-existence of path integrals. Zbl 0745.60051
Lyons, Terry
1991
Instability of the conservative property under quasi-isometries. Zbl 0747.53034
Lyons, Terry
1991
On conditional diffusion processes. Zbl 0715.60097
Lyons, T. J.; Zheng, W. A.
1990
Bases for positive continuous functions. Zbl 0675.30040
Hayman, W. K.; Lyons, T. J.
1990
A synthetic proof of Makarov’s law of the iterated logarithm. Zbl 0708.30033
Lyons, Terry
1990
Diffusion processes with non-smooth diffusion coefficients and their density functions. Zbl 0715.60096
Lyons, T. J.; Zheng, W. A.
1990
A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Zbl 0654.60059
Lyons, Terence J.; Zheng, Weian
1988
Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains. Zbl 0599.60011
Lyons, Terry
1987
The critical dimension at which quasi-every Brownian path is self- avoiding. Zbl 0609.60087
Lyons, Terry J.
1986
Stopping non-commutative processes. Zbl 0585.60058
Barnett, Chris; Lyons, Terry
1986
Function theory, random paths and covering spaces. Zbl 0554.58022
Lyons, Terry; Sullivan, Dennis
1984
Winding of the plane Brownian motion. Zbl 0541.60075
Lyons, T. J.; McKean, H. P.
1984
The best harmonic approximant to a continuous function. Zbl 0541.41024
Hayman, Walter K.; Kershaw, Donald; Lyons, Terry J.
1984
Projection theorems for hitting probabilities and a theorem of Littlewood. Zbl 0566.58036
Lyons, T. J.; MacGibbon, K. B.; Taylor, J. C.
1984
Finely harmonic functions need not be quasi-analytic. Zbl 0541.31002
Lyons, Terry
1984
A simple criterion for transience of a reversible Markov chain. Zbl 0509.60067
Lyons, Terry
1983
Jensen measures for R(K). Zbl 0509.31002
Gamelin, T. W.; Lyons, T. J.
1983
Cones of lower semicontinuous functions and a characterisation of finely hyperharmonic functions. Zbl 0492.31005
Lyons, Terry J.
1982
Finely holomorphic functions. Zbl 0459.46038
Lyons, T. J.
1980
A theorem in fine potential theory and applications to finely holomorphic functions. Zbl 0459.46039
Lyons, T. J.
1980
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### Cited by 993 Authors

 50 Friz, Peter Karl 32 Lyons, Terence John 29 Tindel, Samy 23 Hairer, Martin 20 Gubinelli, Massimiliano 19 Nualart, David 19 Qian, Zhongmin M. 19 Zhang, Tusheng S. 17 Crisan, Dan O. 16 Bailleul, Ismaël F. 15 Inahama, Yuzuru 15 Lejay, Antoine 14 Cass, Thomas Richard 14 Hu, Yaozhong 13 Oberhauser, Harald 13 Russo, Francesco 12 Geng, Xi 12 Riedel, Sebastian 12 Victoir, Nicolas B. 11 Boedihardjo, Horatio 11 Deya, Aurélien 11 Diehl, Joscha 11 Röckner, Michael 10 Müller-Gronbach, Thomas 10 Ouyang, Cheng 10 Teichmann, Josef 10 Yamada, Toshihiro 9 Baudoin, Fabrice 9 Coutin, Laure 9 Prömel, David J. 8 Aida, Shigeki 8 Bayer, Christian 8 Chevyrev, Ilya 8 Fan, Xiliang 8 Litterer, Christian 8 Neuenkirch, Andreas 8 Unterberger, Jérémie M. 8 Zheng, Weian 7 Chen, Zhen-Qing 7 Garrido-Atienza, María José 7 Melbourne, Ian 7 Perkowski, Nicolas 7 Rovira, Carles 7 Xiong, Jie 7 Yaroslavtseva, Larisa 6 Catellier, Rémi 6 Del Moral, Pierre 6 Duc, Luu Hoang 6 Fuglede, Bent 6 Hofmanová, Martina 6 Mazzucchi, Sonia 6 Nilssen, Torstein K. 6 Nourdin, Ivan 6 Ritter, Klaus 6 Zhu, RongChan 5 Albeverio, Sergio A. 5 Besalú, Mireia 5 Beznea, Lucian 5 Brault, Antoine 5 Bruned, Yvain 5 Ebrahimi-Fard, Kurusch 5 Fitzsimmons, Patrick J. 5 Gardiner, Stephen J. 5 Gess, Benjamin 5 Harang, Fabian Andsem 5 Hinz, Michael 5 Ito, Yu 5 Kubilius, Kȩstutis 5 Kuwae, Kazuhiro 5 Liu, Chong 5 Rößler, Andreas 5 Schmalfuß, Björn 5 Tudor, Ciprian A. 5 Weber, Hendrik 5 Yang, Xue 4 Burrage, Kevin 4 da Silva, José Luís 4 Delarue, François 4 Franchi, Jacques 4 Gassiat, Paul 4 Hong, Phan Thanh 4 Kouritzin, Michael A. 4 Kuznetsov, Dmitriĭ Feliksovich 4 Le Jan, Yves 4 León, Jorge A. 4 Liu, Yanghui 4 Manolarakis, Konstantinos 4 Marie, Nicolas 4 Ni, Hao 4 Papavasiliou, Anastasia 4 Peres, Yuval 4 Tapia, Nikolas 4 Vas’kovskiĭ, Maksim Mikhaĭlovich 4 Yang, Danyu 4 Zähle, Martina 4 Zhang, Huilin 4 Zhu, Xiang-Chan 3 Amaba, Takafumi 3 Ancona, Alano 3 Bock, Wolfgang ...and 893 more Authors
all top 5

### Cited in 229 Serials

 87 Stochastic Processes and their Applications 62 The Annals of Probability 53 Journal of Functional Analysis 31 The Annals of Applied Probability 29 Probability Theory and Related Fields 27 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 26 Journal of Differential Equations 21 Potential Analysis 17 Stochastic Analysis and Applications 16 Transactions of the American Mathematical Society 15 Journal of Theoretical Probability 15 Electronic Journal of Probability 15 Bernoulli 14 Journal of Mathematical Analysis and Applications 14 Stochastics and Dynamics 13 Journal of Computational and Applied Mathematics 12 Proceedings of the American Mathematical Society 12 Stochastics 11 Stochastic and Partial Differential Equations. Analysis and Computations 10 Bulletin des Sciences Mathématiques 9 Numerical Algorithms 8 Statistics & Probability Letters 8 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 7 Lithuanian Mathematical Journal 7 Annales de l’Institut Fourier 7 Journal of the Mathematical Society of Japan 7 Journal of Evolution Equations 7 Quantitative Finance 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Communications in Mathematical Physics 6 The Annals of Statistics 6 Journal of Complexity 6 Revista Matemática Iberoamericana 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 6 Discrete and Continuous Dynamical Systems. Series B 5 Communications on Pure and Applied Mathematics 5 Advances in Mathematics 5 Applied Mathematics and Optimization 5 Journal of Applied Probability 5 Proceedings of the Edinburgh Mathematical Society. Series II 5 SIAM Journal on Numerical Analysis 5 Acta Applicandae Mathematicae 5 Applied Numerical Mathematics 5 Acta Mathematicae Applicatae Sinica. English Series 5 Journal of Dynamics and Differential Equations 5 Finance and Stochastics 5 Infinite Dimensional Analysis, Quantum Probability and Related Topics 5 SIAM Journal on Financial Mathematics 4 Journal of Statistical Physics 4 Mathematics of Computation 4 BIT 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Physica D 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Bulletin of the American Mathematical Society. New Series 4 Monte Carlo Methods and Applications 4 Applied Mathematical Finance 4 Discrete and Continuous Dynamical Systems 4 Acta Mathematica Sinica. English Series 4 Annales Henri Poincaré 4 Differential Equations 4 Differentsial’nye Uravneniya i Protsessy Upravleniya 4 ALEA. Latin American Journal of Probability and Mathematical Statistics 4 Science China. Mathematics 4 International Journal of Stochastic Analysis 4 Forum of Mathematics, Sigma 3 Archive for Rational Mechanics and Analysis 3 International Journal of Control 3 Journal of Mathematical Physics 3 Nonlinearity 3 Arkiv för Matematik 3 Inventiones Mathematicae 3 Osaka Journal of Mathematics 3 SIAM Journal on Control and Optimization 3 Journal of Scientific Computing 3 Forum Mathematicum 3 Communications in Partial Differential Equations 3 SIAM Journal on Mathematical Analysis 3 Annals of Mathematics. Second Series 3 Journal of Dynamical and Control Systems 3 Oberwolfach Reports 3 Forum of Mathematics, Pi 2 Advances in Applied Probability 2 Israel Journal of Mathematics 2 Journal of Computational Physics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Collectanea Mathematica 2 Duke Mathematical Journal 2 Mathematische Annalen 2 Mathematics and Computers in Simulation 2 Mathematische Nachrichten 2 Nagoya Mathematical Journal 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the London Mathematical Society. Third Series 2 Tôhoku Mathematical Journal. Second Series 2 Statistical Science 2 Science in China. Series A 2 Japan Journal of Industrial and Applied Mathematics 2 Aequationes Mathematicae 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics ...and 129 more Serials
all top 5

### Cited in 54 Fields

 809 Probability theory and stochastic processes (60-XX) 188 Numerical analysis (65-XX) 134 Partial differential equations (35-XX) 106 Ordinary differential equations (34-XX) 68 Potential theory (31-XX) 64 Systems theory; control (93-XX) 59 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 54 Statistics (62-XX) 47 Global analysis, analysis on manifolds (58-XX) 44 Dynamical systems and ergodic theory (37-XX) 42 Real functions (26-XX) 42 Operator theory (47-XX) 40 Statistical mechanics, structure of matter (82-XX) 37 Functional analysis (46-XX) 23 Functions of a complex variable (30-XX) 22 Quantum theory (81-XX) 19 Measure and integration (28-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 15 Combinatorics (05-XX) 15 Differential geometry (53-XX) 14 Approximations and expansions (41-XX) 13 Associative rings and algebras (16-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 11 Fluid mechanics (76-XX) 10 Computer science (68-XX) 9 Nonassociative rings and algebras (17-XX) 8 Integral equations (45-XX) 6 Topological groups, Lie groups (22-XX) 6 Biology and other natural sciences (92-XX) 5 General and overarching topics; collections (00-XX) 5 Algebraic geometry (14-XX) 5 Information and communication theory, circuits (94-XX) 4 Algebraic topology (55-XX) 4 Operations research, mathematical programming (90-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Group theory and generalizations (20-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Geometry (51-XX) 3 General topology (54-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 Special functions (33-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Category theory; homological algebra (18-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)

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