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