An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations

Wang, Weifeng; Yan, Lei; Hu, Junhao; Guo, Zhongkai

doi:10.1155/2021/8742330

Journal of Mathematics

2021

DOI: 10.1155/2021/8742330

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An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations

Weifeng Wang

Lei Yan

Junhao Hu

et al.

Abstract: In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion. Compared with the classic averaging condition for stochastic differential equation, we propose a new averaging condition and obtain the averaging convergence results for Mckean–Vlasov-type Caputo fractional stochastic differential equations.

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Cited by 2 publications

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Second-order McKean–Vlasov stochastic evolution equation driven by Poisson jumps: Existence, uniqueness and averaging principle

Shi

2024

Stoch. Dyn.

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In this paper, a class of second-order McKean–Vlasov stochastic evolution equations driven by Poisson jumps with non-Lipschitz conditions is considered. The existence and uniqueness of the mild solution are established by means of the Carathéodory approximation technique. Furthermore, an averaging principle is obtained between the solution of the second-order McKean–Vlasov stochastic evolution equation and that of the simplified equation in the mean-square sense.

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Second-order McKean–Vlasov stochastic evolution equation driven by Poisson jumps: Existence, uniqueness and averaging principle

Shi

2024

Stoch. Dyn.

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Mixed Neutral Caputo Fractional Stochastic Evolution Equations with Infinite Delay: Existence, Uniqueness and Averaging Principle

et al. 2022

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The aim of this article is to consider a class of neutral Caputo fractional stochastic evolution equations with infinite delay (INFSEEs) driven by fractional Brownian motion (fBm) and Poisson jumps in Hilbert space. First, we establish the local and global existence and uniqueness theorems of mild solutions for the aforementioned neutral fractional stochastic system under local and global Carathéodory conditions by using the successive approximations, stochastic analysis, fractional calculus, and stopping time techniques. The obtained existence result in this article is new in the sense that it generalizes some of the existing results in the literature. Furthermore, we discuss the averaging principle for the proposed neutral fractional stochastic system in view of the convergence in mean square between the solution of the standard INFSEEs and that of the simplified equation. Finally, the obtained averaging theory is validated with an example.

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An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations

Cited by 2 publications

References 21 publications

Second-order McKean–Vlasov stochastic evolution equation driven by Poisson jumps: Existence, uniqueness and averaging principle

Second-order McKean–Vlasov stochastic evolution equation driven by Poisson jumps: Existence, uniqueness and averaging principle

Mixed Neutral Caputo Fractional Stochastic Evolution Equations with Infinite Delay: Existence, Uniqueness and Averaging Principle

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