Existence and Uniqueness With the Averaging Principle for Solutions to Stochastic Functional Differential Equations Driven by Fractional Brownian Motion

MA Li; CHANG Hong; LIANG Qing

doi:10.21656/1000-0887.460078

Volume 47 Issue 5

May 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(5): 668-686

MA Li, CHANG Hong, LIANG Qing. Existence and Uniqueness With the Averaging Principle for Solutions to Stochastic Functional Differential Equations Driven by Fractional Brownian Motion[J]. Applied Mathematics and Mechanics, 2026, 47(5): 668-686. doi: 10.21656/1000-0887.460078

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Existence and Uniqueness With the Averaging Principle for Solutions to Stochastic Functional Differential Equations Driven by Fractional Brownian Motion

doi: 10.21656/1000-0887.460078

School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P.R. China

Received Date: 2025-04-15
Rev Recd Date: 2026-04-30
Publish Date: 2026-05-01

Abstract

Abstract

The distribution-dependent stochastic functional differential equations, driven simultaneously by a fractional Brownian motion with Hurst index H>1/2 and a Lévy process and with the Markov switching and the random proportional times, were studied. Firstly, the existence and uniqueness of the solutions to the equations were established through the Carathédory approximation. Then, under certain averaging conditions, it is proved that the solution to the distribution-dependent stochastic differential equation is approximated (in the sense of the p-th moment convergence) by the solution of its averaged stochastic functional differential equation.
- stochastic functional differential equation,
- fractional Brownian motion,
- Lévy process,
- averaging principle

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References

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