Prof. Dr. Xue-Mei Li

Profile

Academic positionFull Professor
Research fieldsProbability theory and stochastic processes
Keywordslong range dependence, stochastic partial differential equations, Multi-scale stochastic dynamics, stochastic differential equations, stochastic differential geometry
Honours and awards

1996: Research Fellowship

Current contact address

CountrySwitzerland
CityLausanne
InstitutionEcole Polytechnique Federale de Lausanne (EPFL)
InstituteSchool of Basic Sciences, Institute of Theoretical Physics

Host during sponsorship

Prof. Dr. Sergio AlbeverioFakultät für Mathematik, SFB 237, Ruhr-Universität Bochum, Bochum
Prof. Dr. Sergio AlbeverioAbteilung für Wahrscheinlichkeitstheorie und Statistik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn
Start of initial sponsorship01/03/1997

Programme(s)

1996Humboldt Research Fellowship Programme

Publications (partial selection)

2025Arnaudon, Marc and Li, Xue-Mei and Petko, Benedikt: Coarse Ricci curvature of weighted Riemannian manifolds. In: Trans. Amer. Math. Soc., 2025,
2025Arnaudon, Marc and Li, Xue-Mei and Petko, Benedikt: Coarse extrinsic curvature of {R}iemannian submanifolds. In: Eur. J. Math., 11, 2025, Paper No. 24, 65
2025Gerolla, Luca and Hairer, Martin and Li, Xue-Mei: Fluctuations of stochastic {PDE}s with long-range correlations. In: Ann. Appl. Probab., 35, 2025, 1198--1232
2023Li, Xue-Mei: Effective diffusions with intertwined structures. In: Mat. Contemp., 58, 2023, 264--315
2023Gozlan, N. and Li, Xue-Mei and Madiman, M. and Roberto, C. and Samson, P.-M.: Log-{H}essian and deviation bounds for {M}arkov semi-groups, and regularization effect in {$\Bbb {L}^1$}. In: Potential Anal., 58, 2023, 123--158
2023Chen, Xin and Li, Xue-Mei and Wu, Bo: Logarithmic heat kernel estimates without curvature restrictions. In: Ann. Probab., 51, 2023, 442--477
2023Li, Xue-Mei and Panloup, Fabien and Sieber, Julian: On the (non)stationary density of fractional-driven stochastic differential equations. In: Ann. Probab., 51, 2023, 2056--2085
2022Gehringer, Johann and Li, Xue-Mei: Functional limit theorems for the fractional {O}rnstein-{U}hlenbeck process. In: J. Theoret. Probab., 35, 2022, 426--456
2022Gehringer, Johann and Li, Xue-Mei and Sieber, Julian: Functional limit theorems for {V}olterra processes and applications to homogenization. In: Nonlinearity, 35, 2022, 1521--1557
2022Hairer, Martin and Li, Xue-Mei: Generating diffusions with fractional {B}rownian motion. In: Comm. Math. Phys., 396, 2022, 91--141
2022Li, Xue-Mei and Sieber, Julian: Mild stochastic sewing lemma, {SPDE} in random environment, and fractional averaging. In: Stoch. Dyn., 22, 2022, Paper No. 2240025, 47
2022Li, Xue-Mei and Sieber, Julian: Slow-fast systems with fractional environment and dynamics. In: Ann. Appl. Probab., 32, 2022, 3964--4003
2021Li, Xue-Mei: Hessian formulas and estimates for parabolic {S}chr\"odinger operators. In: J. Stoch. Anal., 2, 2021, Art. 7, 53
2020Hairer, Martin and Li, Xue-Mei: Averaging dynamics driven by fractional {B}rownian motion. In: Ann. Probab., 48, 2020, 1826--1860
2018Li, Xue-Mei: Doubly damped stochastic parallel translations and {H}essian formulas. Stochastic partial differential equations and related fields. Springer, Cham, 2018. 345--357
2018Li, Xue-Mei and Thompson, James: First order {F}eynman-{K}ac formula. In: Stochastic Process. Appl., 128, 2018, 3006--3029
2018Li, Xue-Mei: Generalised {B}rownian bridges: examples. In: Markov Process. Related Fields, 24, 2018, 151--163
2018Li, Xue-Mei: Homogenisation on homogeneous spaces. In: J. Math. Soc. Japan, 70, 2018, 519--572
2018Li, Xue-Mei: Perturbation of conservation laws and averaging on manifolds. Computation and combinatorics in dynamics, stochastics and control. Springer, Cham, 2018. 499--550
2017Li, Xue-Mei: On the semi-classical {B}rownian bridge measure. In: Electron. Commun. Probab., 22, 2017, Paper No. 38, 15
2017Arnaudon, Marc and Li, Xue-Mei: Reflected {B}rownian motion: selection, approximation and linearization. In: Electron. J. Probab., 22, 2017, Paper No. 31, 55
2017Li, Xue-Mei: Strict local martingales: examples. In: Statist. Probab. Lett., 129, 2017, 65--68
2016Li, Xue-Mei: Limits of random differential equations on manifolds. In: Probab. Theory Related Fields, 166, 2016, 659--712
2016Li, Xue-Mei: On hypoelliptic bridge. In: Electron. Commun. Probab., 21, 2016, Paper No. 24, 12
2016Li, Xue-Mei: Random perturbation to the geodesic equation. In: Ann. Probab., 44, 2016, 544--566
2014Chen, Xin and Li, Xue-Mei: Strong completeness for a class of stochastic differential equations with irregular coefficients. In: Electron. J. Probab., 19, 2014, no. 91, 34
2012Li, Xue-Mei: The stochastic differential equation approach to analysis on path space. New trends in stochastic analysis and related topics. World Sci. Publ., Hackensack, NJ, 2012. 207--226
2011Chen, Xin and Li, Xue-Mei and Wu, Bo: A concrete estimate for the weak {P}oincar\'e{} inequality on loop space. In: Probab. Theory Related Fields, 151, 2011, 559--590
2011Li, Xue-Mei: Intertwinned diffusions by examples. Stochastic analysis 2010. Springer, Heidelberg, 2011. 51--71
2011Li, Xue-Mei and Scheutzow, Michael: Lack of strong completeness for stochastic flows. In: Ann. Probab., 39, 2011, 1407--1421
2010Chen, X. and Li, X.-M. and Wu, B.: A spectral gap for the {B}rownian bridge measure on hyperbolic spaces. Progress in analysis and its applications. World Sci. Publ., Hackensack, NJ, 2010. 398--404
2010Chen, Xin and Li, Xue-Mei and Wu, Bo: A {P}oincar\'e{} inequality on loop spaces. In: J. Funct. Anal., 259, 2010, 1421--1442
2010Elworthy, K. David and Le Jan, Yves and Li, Xue-Mei: The geometry of filtering. Birkh\"auser Verlag, Basel, 2010
2008Li, Xue-Mei: An averaging principle for a completely integrable stochastic {H}amiltonian system. In: Nonlinearity, 21, 2008, 803--822
2008Elworthy, K. D. and Li, Xue-Mei: An {$L^2$} theory for differential forms on path spaces. {I}. In: J. Funct. Anal., 254, 2008, 196--245
2007Elworthy, K. D. and Li, Xue-Mei: It\^o{} maps and analysis on path spaces. In: Math. Z., 257, 2007, 643--706
2006Elworthy, K. David and Li, Xue-Mei: Geometric stochastic analysis on path spaces. International {C}ongress of {M}athematicians. {V}ol. {III}. Eur. Math. Soc., Z\"urich, 2006. 575--594
2006Elworthy, K. David and Li, Xue-Mei: Intertwining and the {M}arkov uniqueness problem on path spaces. Stochastic partial differential equations and applications---{VII}. Chapman \& Hall/CRC, Boca Raton, FL, 2006. 89--95
2005Arnaudon, Marc and Li, Xue-Mei: Barycenters of measures transported by stochastic flows. In: Ann. Probab., 33, 2005, 1509--1543
2004Elworthy, K. David and Le Jan, Yves and Li, Xue-Mei: Equivariant diffusions on principal bundles. Stochastic analysis and related topics in {K}yoto. Math. Soc. Japan, Tokyo, 2004. 31--47
2003Elworthy, K. David and Li, Xue-Mei: Gross-{S}obolev spaces on path manifolds: uniqueness and intertwining by {I}t\^o{} maps. In: C. R. Math. Acad. Sci. Paris, 337, 2003, 741--744
2003Li, Xue-Mei and Wang, Feng-Yu: On the compactness of manifolds. In: Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6, 2003, 29--38
2003Elworthy, K. D. and Li, Xue-Mei: Some families of {$q$}-vector fields on path spaces. In: Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6, 2003, 1--27
2000Elworthy, K. D. and Li, Xue-Mei: Special {I}t\^o{} maps and an {$L^2$} {H}odge theory for one forms on path spaces. Stochastic processes, physics and geometry: new interplays, {I} ({L}eipzig, 1999). Amer. Math. Soc., Providence, RI, 2000. 145--162
1999Arnaudon, Marc and Li, Xue-Mei and Thalmaier, Anton: Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps. In: Ann. Inst. H. Poincar\'e{} Probab. Statist., 35, 1999, 765--791
1999Elworthy, K. D. and Le Jan, Y. and Li, Xue-Mei: On the geometry of diffusion operators and stochastic flows. Springer-Verlag, Berlin, 1999
1999Elworthy, K. D. and Li, Xue-Mei and Yor, M.: The importance of strictly local martingales; applications to radial {O}rnstein-{U}hlenbeck processes. In: Probab. Theory Related Fields, 115, 1999, 325--355
1998Elworthy, K. David and Li, Xue-Mei: Bismut type formulae for differential forms. In: C. R. Acad. Sci. Paris S\'er. I Math., 327, 1998, 87--92
1998Elworthy, K. D. and Li, X.-M. and Rosenberg, S.: Bounded and {$L^2$} harmonic forms on universal covers. In: Geom. Funct. Anal., 8, 1998, 283--303
1997Elworthy, K. D. and Le Jan, Yves and Li, Xue-Mei: Concerning the geometry of stochastic differential equations and stochastic flows. New trends in stochastic analysis ({C}haringworth, 1994). World Sci. Publ., River Edge, NJ, 1997. 107--131
1997Elworthy, K. D. and Li, X. M. and Yor, M.: On the tails of the supremum and the quadratic variation of strictly local martingales. S\'eminaire de {P}robabilit\'es, {XXXI}. Springer, Berlin, 1997. 113--125
1996Elworthy, K. D. and Li, Xue-Mei: A class of integration by parts formulae in stochastic analysis. {I}. It\^o's stochastic calculus and probability theory. Springer, Tokyo, 1996. 15--30
1996Li, Xue-Mei and Zhao, H. Z.: Gradient estimates and the smooth convergence of approximate travelling waves for reaction-diffusion equations. In: Nonlinearity, 9, 1996, 459--477
1996Elworthy, K. David and Le Jan, Yves and Li, Xue-Mei: Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups. In: C. R. Acad. Sci. Paris S\'er. I Math., 323, 1996, 921--926
1995Elworthy, K. D. and Li, X.-M.: Derivative flows of stochastic differential equations: moment exponents and geometric properties. Stochastic analysis ({I}thaca, {NY}, 1993). Amer. Math. Soc., Providence, RI, 1995. 565--574
1995Li, Xue-Mei: On extensions of {M}yers' theorem. In: Bull. London Math. Soc., 27, 1995, 392--396
1994Elworthy, K. D. and Li, X.-M.: Differentiation of heat semigroups and applications. Probability theory and mathematical statistics ({V}ilnius, 1993). TEV, Vilnius, 1994. 239--251
1994Elworthy, K. D. and Li, X.-M.: Formulae for the derivatives of heat semigroups. In: J. Funct. Anal., 125, 1994, 252--286
1994Li, Xue-Mei: Properties at infinity of diffusion semigroups and stochastic flows via weak uniform covers. In: Potential Anal., 3, 1994, 339--357
1994Li, Xue-Mei: Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences. In: Probab. Theory Related Fields, 100, 1994, 417--428
1994Li, Xue-Mei: Strong {$p$}-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds. In: Probab. Theory Related Fields, 100, 1994, 485--511
1993Elworthy, K. D. and Li, X.-M. and Rosenberg, Steven: Curvature and topology: spectral positivity. Methods and applications of global analysis. Voronezh. Univ. Press, Voronezh, 1993. 45--60, 156
[2021] \copyright 2021Gehringer, Johann and Li, Xue-Mei: Rough homogenisation with fractional dynamics. Geometry and invariance in stochastic dynamics. Springer, Cham, [2021] \copyright 2021. 137--168