Prof. Dr. Xue-Mei Li

Profil

Derzeitige StellungProfessor W-3 und Äquivalente
FachgebietWahrscheinlichkeitstheorie
Keywordslong range dependence, stochastic partial differential equations, Multi-scale stochastic dynamics, stochastic differential equations, stochastic differential geometry
Auszeichnungen

1996: Research Fellowship

Aktuelle Kontaktadresse

LandSchweiz
OrtLausanne
Universität/InstitutionEcole Polytechnique Federale de Lausanne (EPFL)
Institut/AbteilungSchool of Basic Sciences, Institute of Theoretical Physics

Gastgeber*innen während der Förderung

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
Beginn der ersten Förderung01.03.1997

Programm(e)

1996Humboldt-Forschungsstipendien-Programm

Publikationen (Auswahl)

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