Averaging principle for space-fractional stochastic partial differential equations driven by Lévy white noise and fractional Brownian motion

Yifei Wang; Haibo Gu; Ruya An; Yifei Wang; Haibo Gu; Ruya An

doi:10.3934/math.2025414

AIMS Mathematics

2025, Volume 10, Issue 4: 9013-9033. doi: 10.3934/math.2025414

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Averaging principle for space-fractional stochastic partial differential equations driven by Lévy white noise and fractional Brownian motion

School of Mathematics Science, Xinjiang Normal University, Urumqi, 830017, China

Received: 13 January 2025 Revised: 29 March 2025 Accepted: 08 April 2025 Published: 21 April 2025
MSC : 35R60, 60H15

This paper's main objective was to obtain an averaging principle for space-fractional stochastic partial differential equations (SFPDEs) driven by Lévy space-time white noise and fractional Brownian motion (fBm). By using the fixed point theorem, we first obtained the existence and uniqueness of mild solutions for the given equation. Subsequently, given some appropriate conditions, we proved that the solution of the original equation converges to that of the averaged equation as the time scale $ \epsilon\to 0 $. This greatly decreases the complexity since one can focus on the averaged equation rather than the original equation.
Citation: Yifei Wang, Haibo Gu, Ruya An. Averaging principle for space-fractional stochastic partial differential equations driven by Lévy white noise and fractional Brownian motion[J]. AIMS Mathematics, 2025, 10(4): 9013-9033. doi: 10.3934/math.2025414

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Abstract

This paper's main objective was to obtain an averaging principle for space-fractional stochastic partial differential equations (SFPDEs) driven by Lévy space-time white noise and fractional Brownian motion (fBm). By using the fixed point theorem, we first obtained the existence and uniqueness of mild solutions for the given equation. Subsequently, given some appropriate conditions, we proved that the solution of the original equation converges to that of the averaged equation as the time scale $ \epsilon\to 0 $. This greatly decreases the complexity since one can focus on the averaged equation rather than the original equation.

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