Recent
- Marc Arnaudon, Xue-Mei Li, Benedikt Petko, Coarse Ricci curvature of weighted Riemannian manifolds, 2023
- Xue-Mei Li, Fabien Panloup, Julian Sieber, On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations. To appear: Annals of Probability
- Luca Gerolla, Martin Hairer, and Xue-Mei Li, Fluctuations of stochastic PDEs with long-range correlations, 2023
- Hairer M, Li X-M, Generating diffusions with fractional Brownian motion, Communications in Mathematical Physics, 396, 91-141, https://doi.org/10.1007/s00220-022-04462-2, 2022,
- Li X-M, Chen X, Wu B, Logarithmic heat kernel estimates without curvature restrictions, Annals of Probability, Vol. 51, No. 2, 442-477, DOI: 10.1214/22-AOP1599, 2023
- Li X-M, Sieber J, Slow-fast systems with fractional environment and dynamics, Annals of Applied Probability, Probab. 32(5): 3964-4003 (October 2022). DOI: 10.1214/22-AAP1779
- Gehringer J, Li X-M, 2022, Functional limit theorems for the fractional Ornstein-Uhlenbeck process, Journal of Theoretical Probability, Vol: 35, Pages: 426-456, ISSN: 0894-9840, 2020
- Hairer M, Li X-M, Averaging dynamics driven by fractional Brownian motion, Annals of Probability, Vol: 48, Pages: 1826-1860, ISSN: 0091-1798, DOI: 10.1214/19-AOP1408, 2020
Analysis on Path Spaces
- Elworthy KD, Li X-M, Geometric stochastic analysis on path spaces, International Congress of Mathematicians 2006.
Geometric Stochastic Analysis (Stochastic Analysis on Manifolds)
- Elworthy KD, Li X-M, 1994, Formulae for the derivatives of heat semigroups, Journal of Functional Analysis
- Arnaudon M, Li X-M, 2005, Barycenters of measures transported by stochastic flows, The Annals of Probability, Vol: 33, Pages: 1509-1543, ISSN: 0091-1798
Stochastic Flows
- Li X-M, 1994, Strong $p$-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds, Probability Theory and Related Field
Strict Local martingales
- Elworthy KD, Li X-M, Yor M, 1999, The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes, Probability Theory and Related Fields
Multi-scale analysis with non-Markovian fast systems:
- Li X-M, Gehringer J, 2019, Homogenization with fractional random fields, arXiv:1911.12600.
Multi-scale analysis On manifolds
- Li X-M, 2018, Homogenisation on homogeneous spaces, Journal of Mathematical Society of Japan
- Li X-M, 2016, Random perturbation to the geodesic equation, Annals of Probability
- Li X-M, 2016, Limits of random differential equations on manifolds, Probability Theory and Related Fields
- Li, X-M, An Averaging Principle for a completely integrable stochastic Hamiltonian system, 2008, Nonlinearity 21, 803.