Averaging principles for two-time-scale neutral stochastic delay partial differential equations driven by fractional Brownian motions

Bin Pei, Yong Xu, Min Han

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We prove the validity of averaging principles for two-time-scale neutral stochastic delay partial differential equations (NSDPDEs) driven by fractional Brownian motions (fBms) under two-time-scale formulation. Firstly, in the sense of mean-square convergence, we obtain not only the averaging principles for NSDPDEs involving two-time-scale Markov switching with a single weakly recurrent class but also for the case of two-time-scale Markov switching with multiple weakly irreducible classes. Secondly, averaging principles for NSDPDEs driven by fBms with random delay modulated by two-time-scale Markovian switching are established. We proved that there is a limit process in which the fast changing noise is averaged out. The limit process is substantially simpler than that of the original full fast–slow system.

Original languageEnglish
Pages (from-to)1169-1199
Number of pages31
JournalStochastics
Volume96
Issue number3
DOIs
StatePublished - 2024

Keywords

  • Averaging principles
  • fractional Brownian motions
  • neutral stochastic delay partial differential equations
  • random delay
  • two-time-scale Markov switching

Fingerprint

Dive into the research topics of 'Averaging principles for two-time-scale neutral stochastic delay partial differential equations driven by fractional Brownian motions'. Together they form a unique fingerprint.

Cite this