A Note on Averaging Principles for Fractional Stochastic Differential Equations

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

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4 引用 (Scopus)

摘要

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.

源语言英语
文章编号216
期刊Fractal and Fractional
8
4
DOI
出版状态已出版 - 4月 2024

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