Papers of Xue-Mei Li

Xue-Mei Li's Research Publications

Preprints.

Intertwined Diffusions by Examples, Xue-Mei Li (2010)
The derivative flow for SDEs with non-smooth coefficients. X. Chen and Xue-Mei Li (2010).
Lack of strong completeness for stochastic flows, Xue-Mei Li and Michael Scheutzow (2009). Provisionally accepted by the Annals of Probability.
A Spectral Gap for the Brownian Bridge measure on hyperbolic spaces. To appear 7th ISAAC Congress proceedings. X. Chen, X.-M. Li and B. Wu.
A Concrete Estimate For The Weak Poincare Inequality On Loop Space. X. Chen, X.-M. Li and B. Wu. To appear: Probab. Th. Relat. Fields.

Books

On the geometry of diffusion operators and stochastic flows. K. D. Elworthy, Xue-Mei Li and Y. LeJan. Lecture Notes in Mathematics, volume 1720, Springer-Verlag (1999). Table of contents ; Introduction.
The Geometry of Filtering Forthcoming Book (Preliminary Version, 2008), K. D. Elworthy, Yves Le Jan, and Xue-Mei Li. To appear in Frontiers in Mathematics Series, Birkhauser.

Journal Publications.

A Poincare Inequality on Loop spaces, X. Chen, X.-M. Li and B. Wu. J. of Funct. Anal. vol 259 (2010)
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
An averaging principle for Integrable stochastic Hamiltonian systems, Xue-Mei Li . Nonlinearity 21 (2008) pp.803--822.
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. (2005).
Barycentres of probability measures transported by stochastic flows. M. Arnaudon and Xue-Mei Li. (2005) Annals of Probability, vol 33, No. 4, 1509-1543.
Invariant Diffusions on Principal Bundles. K. D. Elworthy, Y. LeJan, and Xue-Mei Li. In Advanced Studies in Pure Mathematics, `Stochastic Analysis and Related Topics in Kyoto'. 31--47, Adv. Stud. Pure Math., 41, Math. Soc. Japan, Tokyo, 2004.
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)
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).
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.
The importance of strictly local martingales, applications to Orstein-Uhlenbeck processes. K. D. Elworthy, Xue-Mei Li and M. Yor. Probab. Theory and Relat. Fields. vol 115. p.325-355. (1999).
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)
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)
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).
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.
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.
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. Bull. London Math. Soc. Xue-Mei Li. 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.
Properties at infinity of diffusion semigroups and stochastic flows via weak uniform covers. J. Potential Anal. Xue-Mei Li. Vol. 3, 339-357. 1994.
Strong p-completeness of stochastic differential equations and the existence of smooth flows on non-compact manifolds. Probab. Theory Relat. Fields, Xue-Mei Li. 100, 4, 485-511. 1994.
Stochastic differential equations on non-compact manifolds: moment stability and its topological consequences. Probab. Theory Relat. Fields, Xue-Mei Li.100, 4, 417-428. 1994.
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 .
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.

Theses

Stochastic Flows on Noncompact manifolds (1992).
Behaviour at infinity of stochastic solutions and diffusion semi-groups (1989), M.Sc. dissertation.