Edit Profile (opens in new tab) Lyons, Terence John Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0923.34056Lyons, Terry J. 343 1998 System control and rough paths. Zbl 1029.93001Lyons, Terry; Qian, Zhongmin 231 2002 Differential equations driven by rough signals. I: An extension of an inequality of L. C. Young. Zbl 0835.34004Lyons, Terry 97 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 1176.60002Lyons, Terry J.; Caruana, Michael; Lévy, Thierry 85 2007 Cubature on Wiener space. Zbl 1055.60049Lyons, Terry; Victoir, Nicolas 78 2004 Function theory, random paths and covering spaces. Zbl 0554.58022Lyons, Terry; Sullivan, Dennis 76 1984 Variable step size control in the numerical solution of stochastic differential equations. Zbl 0888.60046Gaines, J. G.; Lyons, T. J. 58 1997 A simple criterion for transience of a reversible Markov chain. Zbl 0509.60067Lyons, Terry 48 1983 Integrability and tail estimates for Gaussian rough differential equations. Zbl 1278.60091Cass, Thomas; Litterer, Christian; Lyons, Terry 46 2013 Decomposition of Dirichlet processes and its applications. Zbl 0804.60044Lyons, T. J.; Zhang, T. S. 37 1994 Uniqueness for the signature of a path of bounded variation and the reduced path group. Zbl 1276.58012Hambly, Ben; Lyons, Terry 36 2010 Random generation of stochastic area integrals. Zbl 0805.60052Gaines, J. G.; Lyons, T. J. 29 1994 An extension theorem to rough paths. Zbl 1134.60047Lyons, Terry; Victoir, Nicolas 26 2007 Nonlinear filtering and measure-valued processes. Zbl 0888.93056Crisan, Dan; Lyons, Terry 25 1997 A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Zbl 0654.60059Lyons, Terence J.; Zheng, Weian 24 1988 Integrability of functionals of Dirichlet processes, probabilistic representations of semigroups, and estimates of heat kernels. Zbl 0914.60045Lunt, John; Lyons, T. J.; Zhang, T. S. 23 1998 Lévy area of Wiener processes in Banach spaces. Zbl 1016.60071Ledoux, M.; Lyons, T.; Qian, Z. 22 2002 On conditional diffusion processes. Zbl 0715.60097Lyons, T. J.; Zheng, W. A. 21 1990 Discrete filtering using branching and interacting particle systems. Zbl 0967.93088Crisan, D.; Del Moral, P.; Lyons, T. 21 1999 Winding of the plane Brownian motion. Zbl 0541.60075Lyons, T. J.; McKean, H. P. 21 1984 Convergence of a branching particle method to the solution of the Zakai equation. Zbl 0915.93060Crisan, Dan; Gaines, Jessica; Lyons, Terry 20 1998 Finely holomorphic functions. Zbl 0459.46038Lyons, T. J. 19 1980 A particle approximation of the solution of the Kushner-Stratonovitch equation. Zbl 0951.93068Crisan, D.; Lyons, T. 18 1999 Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains. Zbl 0599.60011Lyons, Terry 18 1987 Efficient and practical implementations of cubature on Wiener space. Zbl 1221.65009Gyurkó, Lajos Gergely; Lyons, Terry J. 17 2011 Extending the Wong-Zakai theorem to reversible Markov processes. Zbl 1010.60070Bass, R. F.; Hambly, B. M.; Lyons, T. J. 17 2002 Physical Brownian motion in a magnetic field as a rough path. Zbl 1390.60257Friz, Peter; Gassiat, Paul; Lyons, Terry 17 2015 Stochastic area for Brownian motion on the Sierpiński gasket. Zbl 0936.60073Hambly, B. M.; Lyons, T. J. 16 1998 High order recombination and an application to cubature on Wiener space. Zbl 1261.65011Litterer, Christian; Lyons, Terence J. 16 2012 The signature of a rough path: uniqueness. Zbl 1347.60094Boedihardjo, Horatio; Geng, Xi; Lyons, Terry; Yang, Danyu 14 2016 The limits of stochastic integrals of differential forms. Zbl 0969.60078Lyons, Terry; Stoica, Lucreţiu 14 1999 Characteristic functions of measures on geometric rough paths. Zbl 1393.60008Chevyrev, Ilya; Lyons, Terry 14 2016 Backward stochastic dynamics on a filtered probability space. Zbl 1238.60064Liang, Gechun; Lyons, Terry; Qian, Zhongmin 13 2011 Flow of diffeomorphisms induced by a geometric multiplicative functional. Zbl 0918.60009Lyons, Terry; Qian, Zhongmin 13 1998 Rough paths, signatures and the modelling of functions on streams. Zbl 1373.93158Lyons, Terry 13 2014 Minimal entropy approximations and optimal algorithms. Zbl 1018.65014Crisan, Dan; Lyons, Terry 13 2002 Evolving communities with individual preferences. Zbl 1321.60204Cass, Thomas; Lyons, Terry 13 2015 On the non-existence of path integrals. Zbl 0745.60051Lyons, Terry 12 1991 Smoothness of Itô maps and diffusion processes on path spaces. I. Zbl 1127.60033Li, Xiang-Dong; Lyons, Terry J. 12 2006 Lévy’s area under conditioning. Zbl 1099.60054Friz, P.; Lyons, T.; Stroock, D. 12 2006 Bases for positive continuous functions. Zbl 0675.30040Hayman, W. K.; Lyons, T. J. 11 1990 On the importance of the Lévy area for studying the limits of functions of converging stochastic processes. Application to homogenization. Zbl 1199.60292Lejay, Antoine; Lyons, Terry 11 2005 The critical dimension at which quasi-every Brownian path is self- avoiding. Zbl 0609.60087Lyons, Terry J. 9 1986 Discretely sampled signals and the rough Hoff process. Zbl 1348.60058Flint, Guy; Hambly, Ben; Lyons, Terry 9 2016 A note on tightness of capacities associated with Dirichlet forms. Zbl 0781.60063Lyons, Terry; Röckner, Michael 9 1992 Flow equations on spaces of rough paths. Zbl 0890.58090Lyons, Terry; Qian, Zhongmin 9 1997 A class of vector fields on path spaces. Zbl 0877.58059Lyons, T. J.; Qian, Z. M. 9 1997 Stopping non-commutative processes. Zbl 0585.60058Barnett, Chris; Lyons, Terry 9 1986 Convergence of non-symmetric Dirichlet processes. Zbl 0888.31005Lyons, Terry; Zhang, Tusheng 8 1996 System control and rough paths. Zbl 1044.93009Lyons, T. J. 8 2002 Inverting the signature of a path. Zbl 1429.70012Lyons, Terry J.; Xu, Weijun 8 2018 Stochastic Jacobi fields and vector fields induced by varying area on path spaces. Zbl 0903.60008Lyons, Terry; Qian, Zhongmin 7 1997 Hyperbolic development and inversion of signature. Zbl 1362.53009Lyons, Terry J.; Xu, Weijun 7 2017 A signed measure on rough paths associated to a PDE of high order: results and conjectures. Zbl 1193.60071Levin, Daniel; Lyons, Terry 7 2009 Instability of the conservative property under quasi-isometries. Zbl 0747.53034Lyons, Terry 6 1991 Dimension-free Euler estimates of rough differential equations. Zbl 1399.60115Boutaib, Youness; Gyurkó, Lajos Gergely; Lyons, Terry; Yang, Danyu 6 2014 Interacting particle systems approximations of the Kushner-Stratonovitch equation. Zbl 0947.60040Crişan, D.; Del Moral, P.; Lyons, T. J. 6 1999 A synthetic proof of Makarov’s law of the iterated logarithm. Zbl 0708.30033Lyons, Terry 5 1990 Diffusion processes with non-smooth diffusion coefficients and their density functions. Zbl 0715.60096Lyons, T. J.; Zheng, W. A. 5 1990 Random thoughts on reversible potential theory. Zbl 0757.31007Lyons, Terry 5 1992 The geometry of the Brownian curve. Zbl 0778.60058Duplantier, B.; Lawler, G. F.; Le Gall, J.-F.; Lyons, T. J. 5 1993 Uncertain volatility and the risk-free synthesis of derivatives. Zbl 1466.91347Lyons, T. J. 5 1995 Rough paths based numerical algorithms in computational finance. Zbl 1198.91229Gyurkó, Lajos Gergely; Lyons, Terry 5 2010 The interpretation and solution of ordinary differential equations driven by rough signals. Zbl 0827.34049Lyons, Terry J. 4 1995 Note on convergence of Dirichlet processes. Zbl 0793.31006Lyons, T. J.; Zhang, T. S. 4 1993 On the radius of convergence of the logarithmic signature. Zbl 1103.60060Lyons, Terry J.; Sidorova, Nadia 4 2006 The best harmonic approximant to a continuous function. Zbl 0541.41024Hayman, Walter K.; Kershaw, Donald; Lyons, Terry J. 4 1984 A theorem in fine potential theory and applications to finely holomorphic functions. Zbl 0459.46039Lyons, T. J. 3 1980 Cones of lower semicontinuous functions and a characterisation of finely hyperharmonic functions. Zbl 0492.31005Lyons, Terry J. 3 1982 Conditional exponential moments for iterated Wiener integrals. Zbl 0961.60053Lyons, Terry; Zeitouni, Ofer 3 1999 Systems controlled by rough paths. Zbl 1125.93026Lyons, Terry 3 2005 Calculus for multiplicative functionals, Itô’s formula and differential equations. Zbl 0862.60043Lyons, T. J.; Qian, Z. M. 3 1996 On Gauss-Green theorem and boundaries of a class of Hölder domains. Zbl 1103.28007Lyons, Terry J.; Yam, Phillip S. C. 3 2006 Projection theorems for hitting probabilities and a theorem of Littlewood. Zbl 0566.58036Lyons, T. J.; MacGibbon, K. B.; Taylor, J. C. 3 1984 Expected signature of Brownian motion up to the first exit time from a bounded domain. Zbl 1350.60086Lyons, Terry; Ni, Hao 3 2015 Kusuoka-Stroock gradient bounds for the solution of the filtering equation. Zbl 1333.60147Crisan, Dan; Litterer, Christian; Lyons, Terry 3 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 1391.60163Chang, Jiawei; Lyons, Terry; Ni, Hao 3 2018 The adaptive patched cubature filter and its implementation. Zbl 1343.60042Lee, Wonjung; Lyons, Terry 2 2016 Rough paths on manifolds. Zbl 1280.58023Cass, Thomas; Litterer, Christian; Lyons, Terry 2 2012 Introducing cubature to filtering. Zbl 1237.93168Litterer, C.; Lyons, T. 2 2011 Cubature on Wiener space continued. Zbl 1187.35299Litterer, Christian; Lyons, Terry 2 2007 Jensen measures for R(K). Zbl 0509.31002Gamelin, T. W.; Lyons, T. J. 2 1983 Finely harmonic functions need not be quasi-analytic. Zbl 0541.31002Lyons, Terry 2 1984 Uniform factorial decay estimates for controlled differential equations. Zbl 1333.60117Boedihardjo, Horatio; Lyons, Terry; Yang, Danyu 2 2015 Numerical method for model-free pricing of exotic derivatives in discrete time using rough path signatures. Zbl 1437.91431Lyons, Terry; Nejad, Sina; Perez Arribas, Imanol 2 2019 An optimal polynomial approximation of Brownian motion. Zbl 1434.60226Foster, James; Lyons, Terry; Oberhauser, Harald 2 2020 Optimal execution with rough path signatures. Zbl 1443.91263Kalsi, Jasdeep; Lyons, Terry; Arribas, Imanol Perez 2 2020 Recovering the pathwise Itô solution from averaged Stratonovich solutions. Zbl 1338.60148Lyons, Terry; Yang, Danyu 1 2016 A uniform estimate for rough paths. Zbl 1296.60155Lyons, Terry J.; Xu, Weijun 1 2013 Kiyoshi Itô (1915–2008). Zbl 1201.60005Lyons, Terence J. 1 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 1284.42082Lyons, Terry J.; Yang, Danyu 1 2013 Smooth rough paths and applications to Fourier analysis. Zbl 1146.26004Hara, Keisuke; Lyons, Terry 1 2007 On the limit of stochastic integrals of differential forms. Zbl 0899.60046Lyons, Terry; Stoica, Lucreţiu 1 1996 On boundary conditions for stochastic evolution equations with an extremally chaotic source. Zbl 0869.60054Albeverio, S.; Lyons, T.; Rozanov, Yu. 1 1995 Continuity in \(\kappa\) in \(\mathrm{SLE}_\kappa\) theory using a constructive method and rough path theory. Zbl 07374667Beliaev, Dmitry; Lyons, Terry J.; Margarint, Vlad 1 2021 Corrigendum to: “Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length”. Zbl 1400.60089Chang, Jiawei; Lyons, Terry; Ni, Hao 1 2018 Continuity in \(\kappa\) in \(\mathrm{SLE}_\kappa\) theory using a constructive method and rough path theory. Zbl 07374667Beliaev, Dmitry; Lyons, Terry J.; Margarint, Vlad 1 2021 An optimal polynomial approximation of Brownian motion. Zbl 1434.60226Foster, James; Lyons, Terry; Oberhauser, Harald 2 2020 Optimal execution with rough path signatures. Zbl 1443.91263Kalsi, Jasdeep; Lyons, Terry; Arribas, Imanol Perez 2 2020 Numerical method for model-free pricing of exotic derivatives in discrete time using rough path signatures. Zbl 1437.91431Lyons, Terry; Nejad, Sina; Perez Arribas, Imanol 2 2019 Inverting the signature of a path. Zbl 1429.70012Lyons, Terry J.; Xu, Weijun 8 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 1391.60163Chang, Jiawei; Lyons, Terry; Ni, Hao 3 2018 Corrigendum to: “Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length”. Zbl 1400.60089Chang, Jiawei; Lyons, Terry; Ni, Hao 1 2018 Hyperbolic development and inversion of signature. Zbl 1362.53009Lyons, Terry J.; Xu, Weijun 7 2017 The signature of a rough path: uniqueness. Zbl 1347.60094Boedihardjo, Horatio; Geng, Xi; Lyons, Terry; Yang, Danyu 14 2016 Characteristic functions of measures on geometric rough paths. Zbl 1393.60008Chevyrev, Ilya; Lyons, Terry 14 2016 Discretely sampled signals and the rough Hoff process. Zbl 1348.60058Flint, Guy; Hambly, Ben; Lyons, Terry 9 2016 The adaptive patched cubature filter and its implementation. Zbl 1343.60042Lee, Wonjung; Lyons, Terry 2 2016 Recovering the pathwise Itô solution from averaged Stratonovich solutions. Zbl 1338.60148Lyons, Terry; Yang, Danyu 1 2016 Physical Brownian motion in a magnetic field as a rough path. Zbl 1390.60257Friz, Peter; Gassiat, Paul; Lyons, Terry 17 2015 Evolving communities with individual preferences. Zbl 1321.60204Cass, Thomas; Lyons, Terry 13 2015 Expected signature of Brownian motion up to the first exit time from a bounded domain. Zbl 1350.60086Lyons, Terry; Ni, Hao 3 2015 Kusuoka-Stroock gradient bounds for the solution of the filtering equation. Zbl 1333.60147Crisan, Dan; Litterer, Christian; Lyons, Terry 3 2015 Uniform factorial decay estimates for controlled differential equations. Zbl 1333.60117Boedihardjo, Horatio; Lyons, Terry; Yang, Danyu 2 2015 Rough paths, signatures and the modelling of functions on streams. Zbl 1373.93158Lyons, Terry 13 2014 Dimension-free Euler estimates of rough differential equations. Zbl 1399.60115Boutaib, Youness; Gyurkó, Lajos Gergely; Lyons, Terry; Yang, Danyu 6 2014 Integrability and tail estimates for Gaussian rough differential equations. Zbl 1278.60091Cass, Thomas; Litterer, Christian; Lyons, Terry 46 2013 A uniform estimate for rough paths. Zbl 1296.60155Lyons, Terry J.; Xu, Weijun 1 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 1284.42082Lyons, Terry J.; Yang, Danyu 1 2013 High order recombination and an application to cubature on Wiener space. Zbl 1261.65011Litterer, Christian; Lyons, Terence J. 16 2012 Rough paths on manifolds. Zbl 1280.58023Cass, Thomas; Litterer, Christian; Lyons, Terry 2 2012 Efficient and practical implementations of cubature on Wiener space. Zbl 1221.65009Gyurkó, Lajos Gergely; Lyons, Terry J. 17 2011 Backward stochastic dynamics on a filtered probability space. Zbl 1238.60064Liang, Gechun; Lyons, Terry; Qian, Zhongmin 13 2011 Introducing cubature to filtering. Zbl 1237.93168Litterer, C.; Lyons, T. 2 2011 Uniqueness for the signature of a path of bounded variation and the reduced path group. Zbl 1276.58012Hambly, Ben; Lyons, Terry 36 2010 Rough paths based numerical algorithms in computational finance. Zbl 1198.91229Gyurkó, Lajos Gergely; Lyons, Terry 5 2010 Kiyoshi Itô (1915–2008). Zbl 1201.60005Lyons, Terence J. 1 2010 A signed measure on rough paths associated to a PDE of high order: results and conjectures. Zbl 1193.60071Levin, Daniel; Lyons, Terry 7 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 1176.60002Lyons, Terry J.; Caruana, Michael; Lévy, Thierry 85 2007 An extension theorem to rough paths. Zbl 1134.60047Lyons, Terry; Victoir, Nicolas 26 2007 Cubature on Wiener space continued. Zbl 1187.35299Litterer, Christian; Lyons, Terry 2 2007 Smooth rough paths and applications to Fourier analysis. Zbl 1146.26004Hara, Keisuke; Lyons, Terry 1 2007 Smoothness of Itô maps and diffusion processes on path spaces. I. Zbl 1127.60033Li, Xiang-Dong; Lyons, Terry J. 12 2006 Lévy’s area under conditioning. Zbl 1099.60054Friz, P.; Lyons, T.; Stroock, D. 12 2006 On the radius of convergence of the logarithmic signature. Zbl 1103.60060Lyons, Terry J.; Sidorova, Nadia 4 2006 On Gauss-Green theorem and boundaries of a class of Hölder domains. Zbl 1103.28007Lyons, Terry J.; Yam, Phillip S. C. 3 2006 On the importance of the Lévy area for studying the limits of functions of converging stochastic processes. Application to homogenization. Zbl 1199.60292Lejay, Antoine; Lyons, Terry 11 2005 Systems controlled by rough paths. Zbl 1125.93026Lyons, Terry 3 2005 Cubature on Wiener space. Zbl 1055.60049Lyons, Terry; Victoir, Nicolas 78 2004 System control and rough paths. Zbl 1029.93001Lyons, Terry; Qian, Zhongmin 231 2002 Lévy area of Wiener processes in Banach spaces. Zbl 1016.60071Ledoux, M.; Lyons, T.; Qian, Z. 22 2002 Extending the Wong-Zakai theorem to reversible Markov processes. Zbl 1010.60070Bass, R. F.; Hambly, B. M.; Lyons, T. J. 17 2002 Minimal entropy approximations and optimal algorithms. Zbl 1018.65014Crisan, Dan; Lyons, Terry 13 2002 System control and rough paths. Zbl 1044.93009Lyons, T. J. 8 2002 Discrete filtering using branching and interacting particle systems. Zbl 0967.93088Crisan, D.; Del Moral, P.; Lyons, T. 21 1999 A particle approximation of the solution of the Kushner-Stratonovitch equation. Zbl 0951.93068Crisan, D.; Lyons, T. 18 1999 The limits of stochastic integrals of differential forms. Zbl 0969.60078Lyons, Terry; Stoica, Lucreţiu 14 1999 Interacting particle systems approximations of the Kushner-Stratonovitch equation. Zbl 0947.60040Crişan, D.; Del Moral, P.; Lyons, T. J. 6 1999 Conditional exponential moments for iterated Wiener integrals. Zbl 0961.60053Lyons, Terry; Zeitouni, Ofer 3 1999 Differential equations driven by rough signals. Zbl 0923.34056Lyons, Terry J. 343 1998 Integrability of functionals of Dirichlet processes, probabilistic representations of semigroups, and estimates of heat kernels. Zbl 0914.60045Lunt, John; Lyons, T. J.; Zhang, T. S. 23 1998 Convergence of a branching particle method to the solution of the Zakai equation. Zbl 0915.93060Crisan, Dan; Gaines, Jessica; Lyons, Terry 20 1998 Stochastic area for Brownian motion on the Sierpiński gasket. Zbl 0936.60073Hambly, B. M.; Lyons, T. J. 16 1998 Flow of diffeomorphisms induced by a geometric multiplicative functional. Zbl 0918.60009Lyons, Terry; Qian, Zhongmin 13 1998 Variable step size control in the numerical solution of stochastic differential equations. Zbl 0888.60046Gaines, J. G.; Lyons, T. J. 58 1997 Nonlinear filtering and measure-valued processes. Zbl 0888.93056Crisan, Dan; Lyons, Terry 25 1997 Flow equations on spaces of rough paths. Zbl 0890.58090Lyons, Terry; Qian, Zhongmin 9 1997 A class of vector fields on path spaces. Zbl 0877.58059Lyons, T. J.; Qian, Z. M. 9 1997 Stochastic Jacobi fields and vector fields induced by varying area on path spaces. Zbl 0903.60008Lyons, Terry; Qian, Zhongmin 7 1997 Convergence of non-symmetric Dirichlet processes. Zbl 0888.31005Lyons, Terry; Zhang, Tusheng 8 1996 Calculus for multiplicative functionals, Itô’s formula and differential equations. Zbl 0862.60043Lyons, T. J.; Qian, Z. M. 3 1996 On the limit of stochastic integrals of differential forms. Zbl 0899.60046Lyons, Terry; Stoica, Lucreţiu 1 1996 Uncertain volatility and the risk-free synthesis of derivatives. Zbl 1466.91347Lyons, T. J. 5 1995 The interpretation and solution of ordinary differential equations driven by rough signals. Zbl 0827.34049Lyons, Terry J. 4 1995 On boundary conditions for stochastic evolution equations with an extremally chaotic source. Zbl 0869.60054Albeverio, S.; Lyons, T.; Rozanov, Yu. 1 1995 Differential equations driven by rough signals. I: An extension of an inequality of L. C. Young. Zbl 0835.34004Lyons, Terry 97 1994 Decomposition of Dirichlet processes and its applications. Zbl 0804.60044Lyons, T. J.; Zhang, T. S. 37 1994 Random generation of stochastic area integrals. Zbl 0805.60052Gaines, J. G.; Lyons, T. J. 29 1994 The geometry of the Brownian curve. Zbl 0778.60058Duplantier, B.; Lawler, G. F.; Le Gall, J.-F.; Lyons, T. J. 5 1993 Note on convergence of Dirichlet processes. Zbl 0793.31006Lyons, T. J.; Zhang, T. S. 4 1993 A note on tightness of capacities associated with Dirichlet forms. Zbl 0781.60063Lyons, Terry; Röckner, Michael 9 1992 Random thoughts on reversible potential theory. Zbl 0757.31007Lyons, Terry 5 1992 On the non-existence of path integrals. Zbl 0745.60051Lyons, Terry 12 1991 Instability of the conservative property under quasi-isometries. Zbl 0747.53034Lyons, Terry 6 1991 On conditional diffusion processes. Zbl 0715.60097Lyons, T. J.; Zheng, W. A. 21 1990 Bases for positive continuous functions. Zbl 0675.30040Hayman, W. K.; Lyons, T. J. 11 1990 A synthetic proof of Makarov’s law of the iterated logarithm. Zbl 0708.30033Lyons, Terry 5 1990 Diffusion processes with non-smooth diffusion coefficients and their density functions. Zbl 0715.60096Lyons, T. J.; Zheng, W. A. 5 1990 A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Zbl 0654.60059Lyons, Terence J.; Zheng, Weian 24 1988 Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains. Zbl 0599.60011Lyons, Terry 18 1987 The critical dimension at which quasi-every Brownian path is self- avoiding. Zbl 0609.60087Lyons, Terry J. 9 1986 Stopping non-commutative processes. Zbl 0585.60058Barnett, Chris; Lyons, Terry 9 1986 Function theory, random paths and covering spaces. Zbl 0554.58022Lyons, Terry; Sullivan, Dennis 76 1984 Winding of the plane Brownian motion. Zbl 0541.60075Lyons, T. J.; McKean, H. P. 21 1984 The best harmonic approximant to a continuous function. Zbl 0541.41024Hayman, Walter K.; Kershaw, Donald; Lyons, Terry J. 4 1984 Projection theorems for hitting probabilities and a theorem of Littlewood. Zbl 0566.58036Lyons, T. J.; MacGibbon, K. B.; Taylor, J. C. 3 1984 Finely harmonic functions need not be quasi-analytic. Zbl 0541.31002Lyons, Terry 2 1984 A simple criterion for transience of a reversible Markov chain. Zbl 0509.60067Lyons, Terry 48 1983 Jensen measures for R(K). Zbl 0509.31002Gamelin, T. W.; Lyons, T. J. 2 1983 Cones of lower semicontinuous functions and a characterisation of finely hyperharmonic functions. Zbl 0492.31005Lyons, Terry J. 3 1982 Finely holomorphic functions. Zbl 0459.46038Lyons, T. J. 19 1980 A theorem in fine potential theory and applications to finely holomorphic functions. Zbl 0459.46039Lyons, T. J. 3 1980 all cited Publications top 5 cited Publications all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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