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




Academic Activities

PhD Students

PhD students: Johann  Gehringer (Winner of Doris Chen Merit Award), Julian Sieber, Benedikt  Petico, Luca Gerola.  I am also second supervisor to  Rhys Steel, Yuriy Shulzhenki,  Xiangfeng Ren, and Francesco Pedulla.

HabilItation Thesis Examined

Isamel Bailleul (Rennes, France)

Jurgen Angst (Rennes, France)

PhD Thesis examined

Aythami Bethencourt de Leon (ICL)

Francesco De Vecchi (Milan, Italy)

Matthew Egginton (Warwick)

Baptiste Huguet (Bordeaux, france)

Peng Lian (Loughborough)

Christian Pangerl (ICL)

PanPan Ren (Swansea)

Pierre Perruchaud (Rennes, France)

So Takao (ICL)

Timothy King (King's College London)

Arman Khaledian (ICL)

EPSRC grant  on `Multi-Scale Stochastic Dynamics with Fractional Noise'.  

We study systems of interacting stochastic processes with on two different time scales  (epsilon and 1 respectively). Typically, the fast motion would have explored its state space exhibiting ergodic properties on the scale of [0,1] of the slower motion. One expects therefore to extract the   averaged influence of the fast motion and obtain an autonomous equation which approximate well the slow motion when the parameter epsilon is small -- this is called the effective dynamics.  We shall focus mainly on stochastic equations driven by fractional Brownian motions, taking on also its rough path nature. This allows for example to model stochastic  processes with long range dependent increments  with regularity structure different from Wiener processes. The fast process is either  Markov process or other non-Markov dynamics.  In the averaging regime, the effective dynamics  departures from the usual stochastic averaging principle.  A reference for this is `Averaging dynamics driven by fractional Brownian motion'  (, where a fractional averaging principle is introduced.  See also Generating diffusions with fractional Brownian motion;    Rough Homogenisation with Fractional Dynamics;   Slow-Fast Systems with Fractional Environment and Dynamics;    Mild Stochastic Sewing Lemma;   SPDE in Random Environment, and Fractional Averaging;  Functional limit theorems for the fractional Ornstein-Uhlenbeck process