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Stochastic Averaging Principle for Two-Time-Scale SDEs with Distribution-Dependent Coefficients Driven by Fractional Brownian Motion

Guangjun Shen, Jiayuan Yin, Jiang-lun Wu

Communications in Mathematics and Statistics, Volume: 13, Issue: 6, Pages: 1445 - 1479

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1007/s40304-023-00364-4

Abstract

In this paper, we derive an averaging principle for a fast-slow system of stochastic differential equations (SDEs) involving distribution dependent coefficients driven by both fractional Brownian motion (fBm) and standard Brownian motion (Bm). We first establish the existence and uniqueness of solut...

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Published in: Communications in Mathematics and Statistics
ISSN: 2194-6701 2194-671X
Published: Springer Nature 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa63504
Abstract: In this paper, we derive an averaging principle for a fast-slow system of stochastic differential equations (SDEs) involving distribution dependent coefficients driven by both fractional Brownian motion (fBm) and standard Brownian motion (Bm). We first establish the existence and uniqueness of solutions of the fast-slow system and the corresponding averaging equation. Then, we show that the slow component strongly converges to the solution of the associated averaged equation.
Keywords: Averaging principle, Fast–slow systems, Fractional Brownian motion, Standard Brownian motion
College: Faculty of Science and Engineering
Funders: This research is supported by the National Natural Science Foundation of China (Grant no. 12071003).
Issue: 6
Start Page: 1445
End Page: 1479

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