Publications

Xue-Mei Li’s recent preprint can be found at the  Arxiv . A reasonably up to date list is here, a list by topic with summary:  Publication by Topics

Also https://orcid.org/0000-0003-1211-0250,   and  Googlescholar  and Research gate

Li X-M, Chen X, Wu B,  2023, Logarithmic heat kernel estimates without curvature restrictions, Annals of Probability, Vol. 51, No. 2, 442-477, DOI: 10.1214/22-AOP1599

Gozlan N, Li X-M, Madiman M, Roberto C, Samson P-M. Samson, 2023, Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in L1, Potential Analysis, 58, 123-158

Li X-M, Sieber J, 2022, Slow-fast systems with fractional environment and dynamics, Annals of Applied Probability, Probab. 32(5): 3964-4003 (October 2022). DOI: 10.1214/22-AAP1779

Hairer M, Li X-M, 2022, Generating diffusions with fractional Brownian motion, Communications in Mathematical Physics, 396, 91-141, https://doi.org/10.1007/s00220-022-04462-2

Li X-M, Sieber J, 2022, Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging, Stochastics and Dynamics, vol. 22, no. 07, 2240025. https://doi.org/10.1142/S0219493722400299

Gehringer J, Li X-M, 2022, Functional limit theorems for the fractional Ornstein-Uhlenbeck process, Journal of Theoretical Probability, Vol: 35, Pages: 426-456, ISSN: 0894-9840

Gehringer J, Li X-M, Sieber J, 2022, Functional limit theorems for volterra processes and applications to homogenization, Nonlinearity, Vol: 35, Pages: 1-37, ISSN: 0951-7715

Li X-M, 2021, Hessian formulas and estimates for parabolic Schrödinger operators, Journal of Stochastic Analysis, Vol: 2, Pages: 1-54, ISSN: 2689-6931

Gehringer J, Li X-M, 2020, Rough homogenisation with fractional dynamics,  arXiv:2011.00075

Gehringer J, Li X-M, 2020, Diffusive and rough homogenisation in fractional noise field, arXiv:2006.11544

Hairer M, Li X-M, 2019, Averaging dynamics driven by fractional Brownian motion, Annals of Probability, Vol: 48, Pages: 1826-1860, ISSN: 0091-1798, DOI: 10.1214/19-AOP1408

Li X-M, Gehringer J, 2019, Homogenization with fractional random fields,  arXiv:1911.12600

Li X-M, 2018, Perturbation of conservation laws and averaging on manifolds, Computation and Combinatorics in Dynamics, Stochastics and Control, Editors: Celledoni, Di Nunno, Ebrahimi-Fard, Munthe-Kaas, Publisher: Springer, Pages: 499-550, ISBN: 978-3-030-01592-3

Li X-M, Thompson J, 2018, First order Feynman-Kac formula, Stochastic Processes and their Applications, Vol: 128, Pages: 3006-3029, ISSN: 0304-4149

Li X-M, 2018, Doubly damped stochastic parallel translations and Hessian formulas, International Conference on Stochastic Partial Differential Equations and Related Fields, Publisher: Springer

Hairer X, 2018, Generalised Brownian bridges: examples, Markov Processes and Related Fields, Vol: 24, Issue 1, Pages: 151-163, ISSN: 1024-2953

Li X-M, 2018, Homogenisation on homogeneous spaces, Journal of Mathematical Society of Japan, Vol: 70, Pages: 519-572, ISSN: 0025-5645

Arnaudon M, Li X-M, 2017, Reflected Brownian motion: selection, approximation and linearization, Electronic Journal of Probability, Vol: 22, Pages: 1-55, ISSN: 1083-6489

Li X-M, 2017, Strict local martingales: Examples, STATISTICS & PROBABILITY LETTERS, Vol: 129, Pages: 65-68, ISSN: 0167-7152

Li X-M, 2017, On the Semi-classical Brownian Bridge Measure, Electronic Communications in Probability, Vol: 22, ISSN: 1083-589X

Li X-M, 2016, Limits of random differential equations on manifolds, Probability Theory and Related Fields, Vol: 166, Pages: 659-712, ISSN: 0178-8051

Li X-M, 2016, On hypoelliptic bridge, Electronic Communications in Probability, Vol: 21, ISSN: 1083-589X

Li X-M, 2016, Random perturbation to the geodesic equation, Annals of Probability, Vol: 44, Pages: 544-566, ISSN: 0091-1798

Chen X, Li X-M, 2014, Strong completeness for a class of stochastic differential equations with irregular coefficients, Electronic Journal of Probability, Vol: 19, ISSN: 1083-6489

Li X-M, 2012, The stochastic differential equation approach to analysis on path space, New trends in stochastic analysis and related topics, Publisher: World Sci. Publ., Hackensack, NJ, Pages: 207-226

Li X-M, Scheutzow M, 2011, Lack of strong completeness for stochastic flows, Annals of Probability, Vol: 39, Pages: 1407-1421, ISSN: 0091-1798

Li X-M, 2011, Intertwinned diffusions by examples, In  Stochastic analysis 2010, Publisher: Springer, Heidelberg, Pages: 51-71

Chen X, Li X-M, Wu B, 2010, A concrete estimate for the weak Poincaré inequality on loop space, Probability Theory and Related Fields, Vol: 151, Pages: 559-590, ISSN: 1432-2064

Chen X, Li X-M, Wu B, 2010, A Poincaré inequality on loop spaces, Journal of Functional Analysis, Vol: 259, Pages: 1421-1442, ISSN: 0022-1236

Chen X, Li X-M, Wu B, 2010, A spectral gap for the Brownian bridge measure on hyperbolic spaces, Progress in analysis and its applications, Publisher: World Sci. Publ., Hackensack, NJ, Pages: 398-404

Elworthy KD, Le Jan Y, Li X-M, 2010, The geometry of filtering, Publisher: Birkhäuser Verlag, Basel, ISBN: 978-3-0346-0175-7

Chen X, Li X-M 2010,   An approximation scheme for SDEs with non-smooth coefficients   Arxiv:1008.0899

Li X-M,  2012 Effective Diffusions with Intertwined Structures Arxiv:1204.3250

Elworthy KD, Li X-M, 2008, An $L^2$ theory for differential forms on path spaces. I, Journal of Functional Analysis, Vol: 254, Pages: 196-245, ISSN: 0022-1236

Li X-M, 2008, An averaging principle for a completely integrable stochastic Hamiltonian system, Nonlinearity, Vol: 21, Pages: 803-822, ISSN: 0951-7715

Li X-M, Elworthy KD, 2007, Geometric stochastic analysis on path spaces, the International Congress of Mathematicians

Elworthy KD, Li X-M, 2007, Itô maps and analysis on path spaces, Mathematische Zeitschrift, Vol: 257, Pages: 643-706, ISSN: 0025-5874

Elworthy KD, Li X-M, 2006, Geometric stochastic analysis on path spaces, International Congress of Mathematicians. Vol. III, Publisher: Eur. Math. Soc., Zürich, Pages: 575-594https://doi.org/10.4171/022-3/30

Elworthy KD, Li X-M, 2006, Intertwining and the Markov uniqueness problem on path spaces, Stochastic partial differential equations and applications—VII, Publisher: Chapman & Hall/CRC, Boca Raton, FL, Pages: 89-95

Arnaudon M, Li X-M, 2005, Barycenters of measures transported by stochastic flows, The Annals of Probability, Vol: 33, Pages: 1509-1543, ISSN: 0091-1798

Arnaudon M, Hairer X, 2004, Barycentres of probability measures transported by stochastic flows, Annals of Probability, ISSN: 0091-1798

Elworthy KD, Le Jan Y, Li X-M, 2004, Equivariant diffusions on principal bundles, Stochastic analysis and related topics in Kyoto, Stochastic Analysis and Related Topics in Kyoto: In honour of Kiyosi Itô Vol 41, pp 31-47 Advanced Studies in Pure Mathematics,  DOI: 10.2969/aspm/04110031

Elworthy KD, Li X-M, 2003, Some families of $q$-vector fields on path spaces, Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol: 6, Pages: 1-27, ISSN: 0219-0257

Li X-M, Wang F-Y, 2003, On the compactness of manifolds, Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol: 6, Pages: 29-38, ISSN: 0219-0257

Elworthy KD, Li X-M, 2003, Gross-Sobolev spaces on path manifolds: uniqueness and intertwining by Itô maps, Comptes Rendus Mathématique. Académie des Sciences. Paris, Vol: 337, Pages: 741-744, ISSN: 1631-073X

Elworthy KD, Li X-M, 2000, Special Itô maps and an $L^2$ Hodge theory for one forms on path spaces, In Stochastic processes, physics and geometry: new interplays, I (Leipzig, 1999), Publisher: Amer. Math. Soc., Providence, RI, Pages: 145-162 ISBN: 0-8218-1959-3

Elworthy KD, Li X-M, Yor M, 1999, The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes, Probability Theory and Related Fields, Vol: 115, Pages: 325-355, ISSN: 0178-8051

Arnaudon M, Li X-M, Thalmaier A, 1999, Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps, Annales de l’Institut Henri Poincaré. Probabilités et Statistiques, Vol: 35, Pages: 765-791, ISSN: 0246-0203

Elworthy KD, Le Jan Y, Li X-M, 1999, On the geometry of diffusion operators and stochastic flows, Publisher: Springer-Verlag, Berlin, ISBN: 3-540-66708-3

Elworthy KD, Li X-M, Rosenberg S, 1998, Bounded and $L^2$ harmonic forms on universal covers, Geometric and Functional Analysis, Vol: 8, Pages: 283-303, ISSN: 1016-443X

Elworthy KD, Li X-M, 1998, Bismut type formulae for differential forms, Comptes Rendus de l’Académie des Sciences. Série I. Mathématique, Vol: 327, Pages: 87-92, ISSN: 0764-4442

Elworthy KD, Le Jan Y, Li X-M, 1997, Concerning the geometry of stochastic differential equations and stochastic flows, New Trends in Stochastic Analysis: Proceedings of a Tanaguchi International Workshop Charingworth Manor September 21-27 1994, Publisher: World Scientific, Pages: 107-131

Elworthy KD, Li XM, Yor M, 1997, On the tails of the supremum and the quadratic variation of strictly local martingales, Séminaire de Probabilités, XXXI, Publisher: Springer, Berlin, Pages: 113-125

Li X-M, Zhao HZ, 1996, Gradient estimates and the smooth convergence of approximate travelling waves for reaction-diffusion equations, Nonlinearity, Vol: 9, Pages: 459-477, ISSN: 0951-7715

Elworthy KD, Le Jan Y, Li X-M, 1996, Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups, Comptes Rendus de l’Académie des Sciences. Série I. Mathématique, Vol: 323, Pages: 921-926, ISSN: 0764-4442

Elworthy KD, Li X-M, 1996, A class of integration by parts formulae in stochastic analysis. I, Itô’s stochastic calculus and probability theory, Publisher: Springer, Tokyo, Pages: 15-30, ISBN: 978-4-431-68532-6  Article

Li X-M, 1995, On extensions of Myers’ theorem, The Bulletin of the London Mathematical Society, Vol: 27, Pages: 392-396, ISSN: 0024-6093

Elworthy KD, Li X-M, 1995, Derivative flows of stochastic differential equations: moment exponents and geometric properties, Stochastic analysis (Ithaca, NY, 1993), Publisher: Amer. Math. Soc., Providence, RI, Pages: 565-574

Li X-M, 1994, Properties at infinity of diffusion semigroups and stochastic flows via weak uniform covers, Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis, Vol: 3, Pages: 339-357, ISSN: 0926-2601

Elworthy KD, Li X-M, 1994, Formulae for the derivatives of heat semigroups, Journal of Functional Analysis, Vol: 125, Pages: 252-286, ISSN: 0022-1236

Li X-M, 1994, Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences, Probability Theory and Related Fields, Vol: 100, Pages: 417-428, ISSN: 0178-8051

Li X-M, 1994, Strong $p$-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds, Probability Theory and Related Fields, Vol: 100, Pages: 485-511, ISSN: 0178-8051

Elworthy KD, Li X-M, 1994, Differentiation of heat semigroups and applications, Probability theory and mathematical statistics: Proceeding of the Sixth Vilnius Conference (1993), Editors: Kubilius, Grigelionis, Pragarauskas, Statulevicius, Publisher: TEV, Vilnius, Pages: 239-251

Elworthy KD, Li X-M, Rosenberg S, 1993, Curvature and topology: spectral positivity, Methods and applications of global analysis, Publisher: Voronezh. Univ. Press, Voronezh, Pages: 45-156

Li X-M, 1992  Stochastic Flows on Non-compact Manifolds   Arxiv:2105.15017