A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations

Qi Wang, Huabin Chen and Chenggui Yuan
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Qi Wang: Department of Mathematics, Nanchang University, Nanchang 330031, China
Huabin Chen: Department of Mathematics, Nanchang University, Nanchang 330031, China
Chenggui Yuan: Department of Mathematics, Bay Campus, Swansea University, Swansea SA1 8EN, UK

Mathematics, 2022, vol. 10, issue 6, 1-11

Abstract: This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler–Maruyama numerical solution to this equation. In addition, the Borel–Cantelli lemma and the stochastic analysis theory are incorporated to discuss the almost sure exponential stability for this numerical solution of such equations.

Keywords: neutral stochastic functional differential equations; Euler–Maruyama method; discrete Razumikhin-type theorem; exponential stability; numerical solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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