A Note on Averaging Principles for Fractional Stochastic Differential Equations

Jiankang Liu, Haodian Zhang, Jinbin Wang, Chen Jin, Jing Li, Wei Xu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Over the past few years, many scholars began to study averaging principles for fractional stochastic differential equations since they can provide an approximate analytical method to reduce such systems. However, in the most previous studies, there is a misunderstanding of the standard form of fractional stochastic differential equations, which consequently causes the wrong estimation of the convergence rate. In this note, we take fractional stochastic differential equations with Lévy noise as an example to clarify these two issues. The corrections herein have no effect on the main proofs except the two points mentioned above. The innovation of this paper lies in three aspects: (i) the standard form of the fractional stochastic differential equations is derived under natural time scale; (ii) it is first proved that the convergence interval and rate are related to the fractional order; and (iii) the presented results contain and improve some well known research achievements.

Original languageEnglish
Article number216
JournalFractal and Fractional
Volume8
Issue number4
DOIs
StatePublished - Apr 2024

Keywords

  • averaging principle
  • convergence rate
  • fractional stochastic differential equations
  • time scale

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