Rough homogenisation with fractional dynamics. (English) Zbl 1499.60335
Ugolini, Stefania (ed.) et al., Geometry and invariance in stochastic dynamics. Selected papers based on the presentations at the the conference on random transformations and invariance in stochastic dynamics, Verona, Italy, March 25–29, 2019. Cham: Springer. Springer Proc. Math. Stat. 378, 137-168 (2021).
Summary: 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.
For the entire collection see [Zbl 1479.37003].
For the entire collection see [Zbl 1479.37003].
MSC:
| 60L20 | Rough paths |
| 60F05 | Central limit and other weak theorems |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |
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