Strong convergence of neutral stochastic functional differential equations with two time-scales

Junhao Hu; Chenggui Yuan

doi:10.3934/dcdsb.2019108

Article Contents

2019, Volume 24, Issue 11: 5831-5848. Doi: 10.3934/dcdsb.2019108

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Strong convergence of neutral stochastic functional differential equations with two time-scales

Junhao Hu^1, and
Chenggui Yuan^2,

1.
College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China
2.
Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, UK

Received: June 30, 2018

Revised: November 30, 2018

Early access: June 2019

Published: August 2019

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Abstract

The purpose of this paper is to discuss the strong convergence of neutral stochastic functional differential equations (NSFDEs) with two time-scales. The existence and uniqueness of invariant measure of the fast component is proved by using Wasserstein distance and the stability-in-distribution argument. The strong convergence between the slow component and the averaged component is also obtained by the the averaging principle in the spirit of Khasminskii's approach.

Keywords:

Two time-scales,
neutral functional differential equations,
exponential ergodicity,
invariant measure,
averaging principle.

Mathematics Subject Classification: 60H10, 60H30.

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