Diffusive and rough homogenisation in fractional noise field
File(s)2006.11544v1.pdf (364.57 KB)
Working paper
Author(s)
Gehringer, Johann
Li, Xue-Mei
Type
Working Paper
Abstract
With recently developed tools, we prove a homogenisation theorem for a random
ODE with short and long-range dependent fractional noise. The effective
dynamics are not necessarily diffusions, they are given by stochastic
differential equations driven simultaneously by stochastic processes from both
the Gaussian and the non-Gaussian self-similarity universality classes. A key
lemma for this is the `lifted' joint functional central and non-central limit
theorem in the rough path topology.
ODE with short and long-range dependent fractional noise. The effective
dynamics are not necessarily diffusions, they are given by stochastic
differential equations driven simultaneously by stochastic processes from both
the Gaussian and the non-Gaussian self-similarity universality classes. A key
lemma for this is the `lifted' joint functional central and non-central limit
theorem in the rough path topology.
Date Issued
2020-06-20
Citation
2020
Publisher
arXiv
Copyright Statement
© 2020 The Author(s)
Identifier
http://arxiv.org/abs/2006.11544v1
Subjects
math.PR
math.PR
34F05, 60F05, 60F17, 60G18, 60G22, 60H05, 60H07, 60H10
Notes
This is the revised second part of arXiv:1911.12600
Publication Status
Published