Mixed stochastic differential equations: Averaging principle result

Min Han, Yong Xu, Bin Pei

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

It is now known that, under a weaker condition than the Lipschitz one, the existence and uniqueness result for solutions of stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter H>1∕2 and a standard Brownian motion is obtained. Therefore, it is quite natural to ask whether or when the averaging principle result also holds. In this paper we study this problem using the tool of generalized Stieltjes integral and Bihari-type lemma.

Original languageEnglish
Article number106705
JournalApplied Mathematics Letters
Volume112
DOIs
StatePublished - Feb 2021

Keywords

  • Averaging principles
  • Fractional Brownian motion
  • Generalized Stieltjes integral
  • Non-Lipschitz condition

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