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Preprints.
Books
Journal Publications.
- A Poincare Inequality on Loop spaces,
X. Chen, X.-M. Li and B. Wu. J. of Funct. Anal. vol 259 (2010)
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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
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An averaging principle for Integrable stochastic Hamiltonian systems, Xue-Mei Li .
Nonlinearity 21 (2008) pp.803--822.
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Itô maps and analysis on path spaces.
K. D. Elworthy and Xue-Mei Li.
Math. Zeitschrift. (2007) 257: pp 643--706.
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Geometric stochastic analysis on path spaces, K. D. Elworthy and Xue-Mei Li. Proceedings of the international Congress of Mathematicians, 575-594 (2006)
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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).
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Barycentres of probability measures transported by stochastic flows.
M. Arnaudon and Xue-Mei Li. (2005) Annals of Probability, vol 33, No. 4, 1509-1543.
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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.
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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).
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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)
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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).
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Hodge de Rham decomposition for an L2 space of differential
2-forms on path spaces. K. D. Elworthy and and Xue-Mei Li. (2002)
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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.
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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).
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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)
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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.
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Bismut type formula for differential forms.
K. D. Elworthy and Xue-Mei Li. C. R. Acad. Sci. t. 327, Série I, 87-92,
(1998)
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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).
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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.
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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.
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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.
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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).
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On extensions of Myers' theorem. Bull.
London Math. Soc. Xue-Mei Li. 27, 392-396. 1995.
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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.
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Properties at infinity of diffusion semigroups and
stochastic flows via weak uniform covers. J. Potential
Anal. Xue-Mei Li. Vol. 3, 339-357. 1994.
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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.
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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.
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Formulae for the derivatives of heat semigroups.
J. Funct. Anal. 125, 1, 252-286. 1994. K. D. Elworthy and Xue-Mei Li.
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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
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