Professor of Mathematics
Chair in Probability and Stochastic Analysis
Department of Mathematics Imperial College London
London SW7 2AZ
U.K.
About Me
I am a Professor of Mathematics at the Imperial College London. Besides teaching,
I also organise seminars, workshops and conferences, and do editorial work
(I am currently an associate Editor of the Electr. J. Probab. and ELectr. C. Probab.).
I am a member of the management committee of the Centre for Doctoral Training on Mathematics of Random Systems.
I work and research in Probability and Stochastic Analysis.
Most of my research work involves stochastic differential equations, diffusion operators, and stochastic processes on 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 with fractional noise.
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
here.
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 Articles
Logarithmic heat kernels: estimates without curvature restrictions, Xin Chen, Xue-Mei Li, Bo Wu. (2021)
Article
Functional Limit Theorems for Volterra Processes and Applications to Homogenization.
Johann Gehringer, Xue-Mei Li, Julian Sieber,(2021).
Article
Slow-Fast Systems with Fractional Environment and Dynamics,(2020), Xue-mei Li and Julian Sieber.
Article
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. (2020)
Article
Homogenization with fractional random fields,
Johann Gehringer and Xue-Mei Li. (2019)
Article
Averaging dynamics driven by fractional Brownian motion.
Martin Hairer and Xue-Mei Li. To appear Ann. Probab. Article
Log-Hessian formula and the Talagrand conjecture
N Gozlan, Xue-Mei Li, M Madiman, C. Roberto, P.-M Samson
(2019)Article
Perturbation of Conservation Laws and Averaging on Manifolds, Xue-Mei Li,
In The Abelsymposium: Computation and Combinatorics in Dynamics, Stochastics and Control. (2018)
Article.
Homogenisation on Homogeneous Spaces (with an appendix by D. Rumynin)
Article 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.
Article
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 ArticleElectronic Journal of Probability 2017, Vol. 22, paper no. 31, 1-55
On the Semi-Classical Brownian Bridge Measure' arxiv:1607.06498 ArticleElectronic Communications in Probability 2017, Vol. 22, paper no. 38, 1-15
Strict Local Martingales: examples.
, Statistics and Probability Letters 129(2017) 65-68.
published version
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
article
On Hypoelliptic bridge. AticleElectronic Communications in Probability,
Vol 24, no 20, 1-12 (2016)
Hessian formulas and estimates for parabolic Schroedinger operators. (2016), Xue-Mei Li, Arxiv