Journal Publications

Preprints

Functional Limit Theorems for Volterra Processes and Applications to Homogenization (2021), article. Johann Gehringer, Xue-Mei Li, Julian Sieber
Slow-Fast Systems with Fractional Environment and Dynamics (2020), article. Xue-Mei Li, Julian Sieber
Rough Homogenisation with Fractional Dynamics (2020), article. Johann Gehringer, Xue-Mei Li
Diffusive and rough homogenisation in fractional noise field(2020), article. Johann Gehringer, Xue-Mei Li
Homogenization with fractional random fields(2019), article. Johann Gehringer, Xue-Mei Li
Log-Hessian formula and the Talagrand conjecture. N Gozlan, Xue-Mei Li, M Madiman, C. Roberto, P.-M Samson (2019) article.
Hessian formulas and estimates for parabolic Schroedinger operators. (2016), Xue-Mei Li, Arxiv

Research Books

On the Geometry of Diffusion Operators and Stochastic Flows. Lecture Notes in Mathematics, volume 1720, Springer-Verlag (1999). K. D. Elworthy, Y. LeJan, and Xue-Mei Li. Introduction
The Geometry of Filtering, Birkhauser, (2010). K. D. Elworthy, Yves Le Jan and Xue-Mei Li.

Other Preprints

An approximation scheme for SDEs with non-smooth coefficients. Xin Chen and Xue-Mei Li (2010)"https://arxiv.org/abs/1008.0899"
Effective Diffusions with Intertwined Structures (2012) Article Arxiv:1204.3250

Other Publications

Functional limit theorems for the fractional Ornstein-Uhlenbeck process (2020), article. Johann Gehringer, Xue-Mei Li. In Journal of Theoretical Probability.
Averaging dynamics driven by fractional Brownian motion (2020) Martin Hairer and Xue-Mei Li. In Ann. Probab. article.
Perturbation of Conservation Laws and Averaging on Manifolds (2017), article. Xue-Mei Li, In Abelsymposium 2016.
Generalised Brownian bridges: examples. In Markov Processes and Related Fields.
Homogenisation on Homogeneous Spaces (with an appendix by D. Rumynin) (2018) Article arXiv:1505.06772. In Journal of the Mathematical Society of Japan. Xue-Mei Li
Doubly Damped Parallel translations and Hessian formulas, '`Stochastic Partial Differential Equations and Related Fields'', `in Honor of Michael Roeckner, SPDERF, Bielefeld, Germany, October 10-14, 2016'. In Springer Proceedings in Mathematics & Statistics, (2018) Xue-Mei Li.
First order Feynman-Kac Formula. Xue-Mei Li and James Thompson,

Stochastic Processes and their applications, doi.org/10.1016/j.spa.2017.10.010.

Reflected Brownian Motion: selection, approximation, and Linearization. M. Arnaudon and Xue-Mei Li. arxiv:1602.00897 Article Electronic Journal of Probability 2017, Vol. 22, paper no. 31, 1-55
On the Semi-Classical Brownian Bridge Measure' arxiv:1607.06498 Article Electronic Communications in Probability 2017, Vol. 22, paper no. 38, 1-15
Strict Local Martingales: examples. , Statistics and Probability Letters 129(2017) 65-68. published version arxiv:1609.00935 Article in Arxiv . Xue-Mei Li.
Limits of Random Differential Equations on Manifolds. Article. Probability Theory Related Fields. Vol 166:659-712, No 3-4 (2016). 10.1007/s00440-015-0669-x arXiv:1501.04793, Xue-Mei Li
Random Perturbation to the geodesic equation. The Annals of Probability , 44(1), 544-566, (2016), Xue-Mei Li. arxiv:1402.5861 article
On Hypoelliptic bridge. Aticle Electronic Communications in Probability, Vol 24, no 20, 1-12 (2016)
Strong completeness for a class of stochastic differential equations with irregular coefficients , X. Chen and Xue-Mei Li. Electronic J. of Probability. 19 (2014) no. 91 1-34. article. also in arXiv:1402.5079
The stochastic differential equation approach to analysis on path space. New trends in stochastic analysis and related topics, 207-226, Xue-Mei Li (2012)
Lack of strong completeness for stochastic flows, Xue-Mei Li and Michael Scheutzow. Annals of Probability, vol 39(4), 1407-1421 (2011).
A Concrete Estimate For The Weak Poincare Inequality On Loop Space. X. Chen, Xue-Mei Li, and B. Wu. Probab. Theory Relat. Fields (2011) 151:559-590
A spectral gap for the Brownian bridge measure on hyperbolic spaces X. Chen, Xue-Mei Li, and B. Wu, Progress in analysis and its applications, 398-404, World Sci. Publ., Hackensack, NJ, 2010.
A Poincare Inequality on Loop spaces, X. Chen, Xue-Mei Li, and B. Wu. J. of Funct. Anal. vol 259 (6), pp 1421-1442 (2010)
Intertwined Diffusions by Examples. Xue-Mei Li. In `Stochastic Analysis 2010', Springer. ed. D. Crisan. (2010)
An averaging principle for Integrable stochastic Hamiltonian systems Nonlinearity 21 (2008) pp.803--822, Xue-Mei Li.
An L2 theory for differential forms on path spaces I, K. D. Elworthy and Xue-Mei Li. J. Funct. Anal. 254(2008) pp.196--245
Itô maps and analysis on path spaces. K. D. Elworthy and Xue-Mei Li. Math. Zeitschrift. (2007) 257: pp 643--706.
Geometric stochastic analysis on path spaces, K. D. Elworthy and Xue-Mei Li. Proceedings of the international Congress of Mathematicians, 575-594 (2006)
Intertwining and the Markov uniqueness problem on path spaces K. D. Elworthy and Xue-Mei Li. In Stochastic Partial Differential Equations and Applications - VII, eds G. Da Prato, L. Tubaro. (2006).
Barycentres of probability measures transported by stochastic flows. M. Arnaudon and Xue-Mei Li. (2005) Annals of Probability, vol 33, No.4, 1509-1543.
Equi-variant Diffusions on Principal Bundles. K. D. Elworthy, Y. LeJan, and Xue-Mei Li. In Advanced Studies in Pure Mathematics, 31--47, 41, `Stochastic Analysis and Related Topics in Kyoto'. Math. Soc. Japan, Tokyo, 2004.
Gross-Sobolev spaces on path manifolds: uniqueness and intertwining by Itô maps. K. D. Elworthy and Xue-Mei Li. C. R. Acad. Sci. Paris, Ser. I 337 (2003) 741-744.
Some Families of q-vector fields on path spaces K. D. Elworthy and Xue-Mei Li. Infinite Dimensional Analysis, Quantum Probability and Related Topics. Volume 6, pages 1-27 (2003).
On compactness of manifolds and existence of certain type functional inequalities. Xue-Mei Li and F.-Y. Wang. Infinite Dimensional Analysis, Quantum Probability and Related Topics. Volume 6, pages 29-38, (2003).
Large time asymptotics of Barycentres of Brownian motions on Hyperbolic spaces M. Arnaudon and Xue-Mei Li. In Analyse Stochastique et Theorie du Potential. (2003)
Hodge de Rham decomposition for an L2 space of differential 2-forms on path spaces. K. D. Elworthy and and Xue-Mei Li. (2002)
Special Itô maps and an L2 Hodge theory for one forms on path spaces. K. D. Elworthy and Xue-Mei Li. Stochastic processes, physics and geometry: new interplays, I (Leipzig, 1999), 145--162, CMS Conf. Proc., 28, Amer. Math. Soc., Providence, RI, 2000.
Manifold-valued martingales, change of probabilities, and smoothness of finely harmonic maps. M. Arnaudon, Xue-Mei Li and and A. Thalmaier. Annals of Institute Henri Poincare. Vol. 35, no. 6, p.765-791. (1999)
The importance of strictly local martingales, applications to Ornstein-Uhlenbeck processes. K. D. Elworthy, Xue-Mei Li and M. Yor. Probab. Theory and Relat. Fields. vol 115. p.325-355. (1999).
Bounded and L^2 Harmonic Forms on Universal Covers. Geom. And Funct. Anal. Vol. 8 , 283-303 (1998). K. D. Elworthy, Xue-Mei Li and and S. Rosenberg.
Bismut type formula for differential forms. K. D. Elworthy and Xue-Mei Li. C. R. Acad. Sci. t. 327, Série I, 87-92, (1998)
On the tails of the supremum and the quadratic variation of strictly local martingales . K. D. Elworthy, Xue-Mei Li and M. Yor. Sem. prob. XXXI, LNM 1655, June 1997.
Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups. C. R. Acad. Sci. t.323 série 1, p. 921-926 (1997). K. D. Elworthy, Yves LeJan and and Xue-Mei Li.
Concerning the geometry of stochastic differential equations and stochastic flows. In 'New Trends in Stochastic Analysis', Proc. Taniguchi Symposium, Sept. 1995, Charingworth, ed. K. D. Elworthy and S. Kusuoka, I. Shigekawa, World Scientific Press. K. D. Elworthy, Yves Le Jan, Xue-Mei Li (1997).
Gradient estimates and the smooth convergence of approximate travelling waves for reaction-diffusion equations. Nonlinearity, 9, 459-477 (1996). Xue-Mei Li and H. Z. Zhao.
A class of Integration by parts formulae in stochastic analysis I. Itô's Stochastic Calculus and Probability Theory (dedicated to Itô on the occasion of his eightieth birthday) , ed. S. Watanabe. K. D. Elworthy and Xue-Mei Li. Springer, (1996).
On extensions of Myers' theorem. Xue-Mei Li. Bull. London Math. Soc. 27, 392-396. 1995.
Derivative flows of stochastic differential equations: moment exponents and geometric properties. Stochastic Analysis. In AMS Proceedings of Symposia in Pure Mathematics. Eds. Cranston, M. G. and Pinsky, M. A. p. 565-574. 1995. K. D. Elworthy and Xue-Mei Li.
Formulae for the derivatives of heat semigroups. J. Funct. Anal. 125, 1, 252-286. 1994. K. D. Elworthy and Xue-Mei Li.
Differentiation of heat semigroups and applications. Probability Theory and Mathematics Stats (Proc. 6th Vilnius conferences). Eds. B. Grigelionis et al. VSP/TEV, Utrecht and Vilnius. In New Titles in Probability and Statistics Series. p. 239-251. 1994. K. D. Elworthy and Xue-Mei Li.
Stochastic differential equations on non-compact manifolds: moment stability and its topological consequences, Xue-Mei Li. Probab. Theory Relat. Fields. 100, 4, 417-428. 1994.
Strong p-completeness of stochastic differential equations and the existence of smooth flows on non-compact manifolds. Probab. Theory Relat. Fields. 100, 4, 485-511. 1994, Xue-Mei Li.
Properties at infinity of diffusion semigroups and stochastic flows via weak uniform covers. J. Potential Anal. Vol. 3, 339-357. 1994, Xue-Mei Li.
Curvature and topology: spectral positivity. Methods and Applications of Global Analysis, Ed. Yu Gliklikh. In Voronezh Series on New Developments in Global Analysis.p. 45-60. 1993. K. D. Elworthy, Xue-Mei Li and Steven Rosenberg.
Stochastic Flows on Noncompact Manifolds. Ph.D. thesis (1992).
Behaviour at infinity of stochastic solutions and diffusion semi-groups. M.Sc. Dissertation (1989).

Preprints and publications

Preprints

Research Books

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