An effective averaging theory for fractional neutral stochastic equations of order \(0 < \alpha < 1\) with Poisson jumps

DOI10.1016/j.aml.2020.106344zbMath1462.60081OpenAlexW3012131204MaRDI QIDQ2178682

Wei Xu, Wenjing Xu

Publication date: 11 May 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106344

zbMATH Keywords

averaging principlefractional orderPoisson jumpsneutral stochastic systems

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05)

Related Items (6)

An averaging principle for neutral stochastic fractional order differential equations with variable delays driven by Lévy noise ⋮ Continuity and approximation properties of solutions to fractional neutral stochastic functional differential equations with non-Lipschitz coefficients ⋮ The existence and averaging principle for stochastic fractional differential equations with impulses ⋮ The averaging principle of Hilfer fractional stochastic delay differential equations with Poisson jumps ⋮ An averaging principle for fractional stochastic differential equations with Lévy noise ⋮ An averaging result for impulsive fractional neutral stochastic differential equations

Cites Work

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• Stochastic averaging principle for dynamical systems with fractional Brownian motion
• Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay
• Integration by parts formula for regional fractional Laplacian
• An averaging principle for stochastic differential delay equations with fractional Brownian motion
• The averaging principle for stochastic differential equations with Caputo fractional derivative
• An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure
• Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
• A new type of the Gronwall-Bellman inequality and its application to fractional stochastic differential equations

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