Theoretical and numerical analysis of the Euler-Maruyama method for generalized stochastic Volterra integro-differential equations

DOI10.1016/J.CAM.2019.112364OpenAlexW2965242749WikidataQ127409121 ScholiaQ127409121MaRDI QIDQ2332678

Jianfang Gao, Hui Liang, Wei Zhang

Publication date: 5 November 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2019.112364

zbMATH Keywords

strong convergenceHölder continuityexistence and uniquenessstochastic Volterra integro-differential equationsEuler-Maruyama method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Stochastic integral equations (60H20)

Related Items (9)

Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion ⋮ Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations ⋮ Convergence of the balanced Euler method for a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients ⋮ Singular stochastic Volterra integral equations with Mittag–Leffler kernels: well-posedness and strong convergence of θ-Maruyama method ⋮ Stochastic maximum principle for moving average control system ⋮ Stability of the analytic solution and the partially truncated Euler–Maruyama method for a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients ⋮ Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method ⋮ Numerical analysis of the balanced methods for stochastic Volterra integro-differential equations ⋮ Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations

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