Approximation properties for solutions to Itô–Doob stochastic fractional differential equations with non-Lipschitz coefficients

DOI10.1142/S0219493719500291zbMath1422.34011OpenAlexW2900389239MaRDI QIDQ5228831

Ji Li, Mahmoud Abouagwa

Publication date: 13 August 2019

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493719500291

zbMATH Keywords

stochastic differential equationsfractional calculusnon-Lipschitz conditionapproximation theoremsCarathéodory approximation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Averaging method for ordinary differential equations (34C29) Ordinary differential equations and systems with randomness (34F05) Fractional ordinary differential equations (34A08)

Related Items (18)

Optimal index and averaging principle for Itô–Doob stochastic fractional differential equations ⋮ Periodic averaging method for impulsive stochastic dynamical systems driven by fractional Brownian motion under non-Lipschitz condition ⋮ Impulsive stochastic fractional differential equations driven by fractional Brownian motion ⋮ Stability of a non-Lipschitz stochastic Riemann-Liouville type fractional differential equation driven by Lévy noise ⋮ An averaging principle for neutral stochastic fractional order differential equations with variable delays driven by Lévy noise ⋮ Existence and stability results for Caputo fractional stochastic differential equations with Lévy noise ⋮ Continuity and approximation properties of solutions to fractional neutral stochastic functional differential equations with non-Lipschitz coefficients ⋮ Existence, uniqueness, and averaging principle for Hadamard Itô–Doob stochastic delay fractional integral equations ⋮ Hadamard Itô-Doob stochastic fractional order systems ⋮ Ulam–Hyers stability of fractional Itô–Doob stochastic differential equations ⋮ Existence and finite-time stability results for impulsive Caputo-type fractional stochastic differential equations with time delays ⋮ The averaging principle of Hilfer fractional stochastic delay differential equations with Poisson jumps ⋮ Stochastic fractional differential equations driven by Lévy noise under Carathéodory conditions ⋮ An averaging result for impulsive fractional neutral stochastic differential equations ⋮ An averaging principle for stochastic fractional differential equations with time-delays ⋮ \(G\)-neutral stochastic differential equations with variable delay and non-Lipschitz coefficients ⋮ Some results on finite-time stability of stochastic fractional-order delay differential equations ⋮ Averaging principle and stability of hybrid stochastic fractional differential equations driven by Lévy noise

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