No Cover Image

Journal article 642 views 121 downloads

Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle

Min Han, Yong Xu, Bin Pei, Jiang-lun Wu Orcid Logo

Journal of Mathematical Analysis and Applications, Volume: 510, Issue: 2, Start page: 126004

Swansea University Author: Jiang-lun Wu Orcid Logo

  • Accepted version JMAA-21-1586.pdf

    PDF | Accepted Manuscript

    ©2022 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND)

    Download (357.73KB)

Check full text

DOI (Published version): 10.1016/j.jmaa.2022.126004

Abstract

The main goal of this article is to study an averaging principle for a class of two-time-scale stochastic differential delay equations in which the slow-varying process includes a multiplicative fractional Brownian noise with Hurst parameter H ∈ (12,1) and the fast-varying process is a rapidly-chang...

Full description

Published in: Journal of Mathematical Analysis and Applications
ISSN: 0022-247X
Published: Elsevier BV 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa59044
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: The main goal of this article is to study an averaging principle for a class of two-time-scale stochastic differential delay equations in which the slow-varying process includes a multiplicative fractional Brownian noise with Hurst parameter H ∈ (12,1) and the fast-varying process is a rapidly-changing diffusion. We would like to emphasize that the approach proposed in this paper is based on the fact that a stochastic integral with respect to fractional Brownian motion with Hurst parameter in (12,1) can be defined as a generalized Stieltjes integral. In particular, to prove a limit theorem for the averaging principle, we will introduce a sequence of stopping times to control the size of multiplicative fractional Brownian noise. Then, inspired by the Khasminskii’s approach, an averaging principle is developed in the sense of convergence in the p-th moment uniformly in time.
Keywords: Averaging principle; Two-time-scaleStochastic differential delay equations; Multiplicative fractional Brownian noise.
College: Faculty of Science and Engineering
Issue: 2
Start Page: 126004

Similar Items