BibTex format
@unpublished{Li:2021,
author = {Li, X-M and Hairer, M},
publisher = {ArXiv},
title = {Generating diffusions with fractional Brownian motion},
url = {https://arxiv.org/abs/2109.06948},
year = {2021}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - We study fast / slow systems driven by a fractional Brownian motion B with Hurst parameter H∈(13,1]. Surprisingly, the slow dynamic converges on suitable timescales to a limiting Markov process and we describe its generator. More precisely, if Yε denotes a Markov process with sufficiently good mixing properties evolving on a fast timescale ε1, the solutions of the equationdXε=ε12−HF(Xε,Yε)dB+F0(Xε,Yε)dtconverge to a regular diffusion without having to assume that F averages to 0, provided that H<12. For H>12, a similar result holds, but this time it does require F to average to 0. We also prove that the n-point motions converge to those of a Kunita type SDE. One nice interpretation of this result is that it provides a continuous interpolation between the homogenisation theorem for random ODEs with rapidly oscillating right-hand sides (H=1) and the averaging of diffusion processes (H=12).
AU - Li,X-M
AU - Hairer,M
PB - ArXiv
PY - 2021///
TI - Generating diffusions with fractional Brownian motion
UR - https://arxiv.org/abs/2109.06948
UR - http://hdl.handle.net/10044/1/92639
ER -