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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

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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...

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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
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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

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