Summary
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' ( https://arxiv.org/abs/1902.11251), 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