Rough Homogenisation with Fractional Dynamics

Abstract: We review recent developments of slow/fast stochastic differential equations, and also present a new result on Diffusion Homogenisation Theory with fractional and non-strong-mixing noise and providing new examples. The emphasise of the review will be on the recently developed effective dynamic theory for two scale random systems with fractional noise: Stochastic Averaging and `Rough Diffusion Homogenisation Theory'. We also study the geometric models with perturbations to symmetries.