Imperial College London

Professor Xue-Mei Li

Faculty of Natural SciencesDepartment of Mathematics

Chair in Probability and Stochastic Analysis



+44 (0)20 7594 Website CV




6M51Huxley BuildingSouth Kensington Campus





I study stochastic processes. My research is supported by :the EPSRC  grant ` Multi-Scale Stochastic Dynamics with Fractional Noise' EP/V026100/1 (PI, 2021- 2024), and also  EPSRC Centre for Doctoral Training  in Mathematics of Random Systems: Analysis, Modelling and Simulation, EP/S023925/1 (Co-I, 2019-2027).

Personal website    Preprints on Arxiv   Publication by Topics . 


 Workshop On Geometry, Stochastics, and Dynamics -- an UK-Japan Winter School celebration event,  September 12-16, 2022.  Conference Webpage


Both PhD and postdoc positions will be open shortly, to work with me at EPFL (Lausanne, Switzerland), please raise enquiry with  me.

 Our Working Seminar

   list               Access-to-Schedule

Here we enjoy mathematics without time pressure. We learn cutting edge techniques as well as classical tools and develop intuition by getting our hands dirty. Speakers present one focused topic in great detail encouraging collaboration. 

Books and lecture notes

The Geometry fo Filtering.    with K.D. Elworthy and  Y. LeJan, Arxiv version:  pdf

On the geometry of diffusion operators and stochastic flows  with K.D. Elworthy and  Y. LeJan. A preliminary version   pdf

Lecture Notes

Markov Processes (2021)    Markov Processes (2020)

Measure and Integration            Stochastic Analysis



Hairer M, Li X-M, 2022, Generating diffusions with fractional Brownian motion, Communications in Mathematical Physics

Li X-M, Sieber J, 2022, Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging, Stochastics and Dynamics, ISSN:0219-4937

Gehringer J, Li X-M, 2022, Functional limit theorems for the fractional Ornstein-Uhlenbeck process, Journal of Theoretical Probability, Vol:35, ISSN:0894-9840, Pages:426-456

Li X-M, Sieber J, 2022, Slow-fast systems with fractional environment and dynamics, Annals of Applied Probability, ISSN:1050-5164

Gehringer J, Li X-M, Sieber J, 2022, Functional limit theorems for volterra processes and applications to homogenization, Nonlinearity, ISSN:0951-7715

More Publications