The averaging principle for stochastic differential equations with Lévy noise involving conformable fractional derivative

Yuan Yuan; Guanli Xiao; Lulu Ren; Yuan Yuan; Guanli Xiao; Lulu Ren

doi:10.3934/math.2025882

AIMS Mathematics

2025, Volume 10, Issue 8: 19775-19794. doi: 10.3934/math.2025882

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The averaging principle for stochastic differential equations with Lévy noise involving conformable fractional derivative

1.
Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
2.
Gui'an Kechuang Company & Guizhou University Joint Data Shield Laboratory, Guiyang, Guizhou 550025, China
3.
School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan, Hubei 430200, China

Received: 15 June 2025 Revised: 12 August 2025 Accepted: 19 August 2025 Published: 28 August 2025
MSC : 26A33, 34A37

In this paper, the averaging principle for conformable fractional stochastic differential equations with Lévy noise is investigated. Initially, the averaging principle for classical Itô-type conformable fractional stochastic differential equations is presented. Subsequently, the averaging principle is extended to the case involving Lévy noise. Different from the approach of integration by parts or decomposing integral interval to deal with the estimation of integral involving singular kernel, this study introduces a novel method to assess the error between the averaged stochastic equation and the original stochastic differential equations, thereby effectively addressing the challenge posed by singular kernels. Finally, a simulation example is provided to validate the theoretical analysis.
- averaging principle,
- conformable fractional derivative,
- stochastic differential equations,
- Lévy noise
Citation: Yuan Yuan, Guanli Xiao, Lulu Ren. The averaging principle for stochastic differential equations with Lévy noise involving conformable fractional derivative[J]. AIMS Mathematics, 2025, 10(8): 19775-19794. doi: 10.3934/math.2025882

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Abstract

In this paper, the averaging principle for conformable fractional stochastic differential equations with Lévy noise is investigated. Initially, the averaging principle for classical Itô-type conformable fractional stochastic differential equations is presented. Subsequently, the averaging principle is extended to the case involving Lévy noise. Different from the approach of integration by parts or decomposing integral interval to deal with the estimation of integral involving singular kernel, this study introduces a novel method to assess the error between the averaged stochastic equation and the original stochastic differential equations, thereby effectively addressing the challenge posed by singular kernels. Finally, a simulation example is provided to validate the theoretical analysis.

References

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