Professor of Mathematics
Chair in Probability and Stochastic Analysis
Department of Mathematics
Imperial College London
London SW7 2AZ
My research focuses on Probability and Stochastic Analysis, involving stochastic differential equations,
diffusion operators, stochastic dynamical systems, and manifolds.
I am fascinated with the large time asymptotics of stochastic processes and its intrinsic geometry.
One of my recent interests is two scale stochastic systems of equations, and Non-Markovian dynamics
with fractional noise. I am involved with the doctor training center `Mathematics of Random Systems',
an associate editor for the Electronic J. of Probability'`and `Electronic Communications in Probability'.`
My Arxiv page can be found at
Xue-Mei Li at arXiv. A set of lecture notes on Markov Processes can be found here.
and also lecture notes on Measure and Integration .
For my public personal web page at Imperial college, click
Please click here fro a list of my research articles ,
and here for a list of my research articles by topics .
These are not regular updated, unfortunately.
Research is supported by EPSRC (EP/S023925/1, EP/S023925/1).
3-year EPSRC funded postdoc position on
Multi-Scale Stochastic Dynamics with Fractional Noise
will be available from September 2021 or after (informal enquiries are welcome)
- Generating diffusions with fractional Brownian motion, Martin Hairer and Xue-Mei Li, 2021.
- Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging,
Xue-Mei Li and Julian Sieber, 2021
- Logarithmic heat kernels: estimates without curvature restrictions, Xin Chen, Xue-Mei Li, Bo Wu. (2021)
- Functional Limit Theorems for Volterra Processes and Applications to Homogenization.
Johann Gehringer, Xue-Mei Li, Julian Sieber (2021). To appear: Nonlinearity
- Slow-Fast Systems with Fractional Environment and Dynamics,(2020)
To appear: Annals of Applied Probability.
Xue-mei Li and Julian Sieber.
Diffusive and rough homogenisation in fractional noise field
Johann Gehringer, Xue-Mei Li. Article (2020)
- Functional limit theorems for the fractional Ornstein-Uhlenbeck process.
Johann Gehringer, Xue-Mei Li.
Journal of Theoretical Probability (2020) Doi: https://doi.org/10.1007/s10959-020-01044-7
Averaging dynamics driven by fractional Brownian motion.
Martin Hairer and Xue-Mei Li.
Ann. Probab. 48(4): 1826-1860, (July 2020). DOI: 10.1214/19-AOP1408.
- Rough Homogenisation with Fractional Dynamics. To appear:
Geometry and Invariance in Stochastic Dynamics, Springer Proceedings.
Johann Gehringer and Xue-Mei Li. (2020)
- Homogenization with fractional random fields,
Johann Gehringer and Xue-Mei Li. (2019)
Log-Hessian formula and the Talagrand conjecture
N Gozlan, Xue-Mei Li, M Madiman, C. Roberto, P.-M Samson. To appear: Potential Analysis.
Perturbation of Conservation Laws and Averaging on Manifolds, Xue-Mei Li,
In The Abelsymposium: Computation and Combinatorics in Dynamics, Stochastics and Control. (2018)
- Homogenisation on Homogeneous Spaces (with an appendix by D. Rumynin)
arXiv:1505.06772. J. Math. Soc. Japan Volume 70, Number 2 (2018), 519-572.
(2018). Xue-Mei Li
- Generalised Brownian bridges: examples. Markov Processes and Related Fields, 2018, v.24, Issue 1, 151-163.
- Doubly Damped Parallel translations and Hessian formulas, In
'`Stochastic Partial Differential Equations and Related Fields'',
`in Honor of Michael Roeckner, SPDERF, Bielefeld, Germany, October 10-14, 2016'. In Springer Proceedings in Mathematics & Statistics, (2018)
Xue-Mei Li. Article"
First order Feynman-Kac Formula. Xue-Mei Li and James Thompson, Stochastic Processes and their applications, doi.org/10.1016/j.spa.2017.10.010.
Volume 128, Issue 9, September 2018, Pages 3006-3029.
Article in journal,
Article in arxiv
- Reflected Brownian Motion: selection, approximation, and Linearization. M. Arnaudon and Xue-Mei Li. arxiv:1602.00897 Article Electronic Journal of Probability 2017, Vol. 22, paper no. 31, 1-55
- On the Semi-Classical Brownian Bridge Measure' arxiv:1607.06498 Article
Electronic Communications in Probability 2017, Vol. 22, paper no. 38, 1-15
- Strict Local Martingales: examples.
, Statistics and Probability Letters 129(2017) 65-68.
arxiv:1609.00935 Article in Arxiv . Xue-Mei Li.
- Limits of Random Differential Equations on Manifolds. Article. Probability Theory Related Fields. Vol 166:659-712, No 3-4 (2016). 10.1007/s00440-015-0669-x arXiv:1501.04793, Xue-Mei Li
Random Perturbation to the geodesic equation. The Annals of Probability , 44(1), 544-566, (2016), Xue-Mei Li. arxiv:1402.5861
- On Hypoelliptic bridge. Aticle Electronic Communications in Probability,
Vol 24, no 20, 1-12 (2016)
- Hessian formulas and estimates for parabolic Schroedinger operators. (2016), Xue-Mei Li, Arxiv