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

Abstract

In this paper, we develop the partially truncated Euler–Maruyama method of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients. The mean-square exponential stability and the mean-square stability of the analytic solution and the partially truncated Euler–Maruyama method are investigated. Moreover, the theoretical results are illustrated by some numerical examples.

Keywords:

• Stochastic Volterra integro-differential equations
• non-globally Lipschitz condition
• partially truncated Euler–Maruyama method
• mean-square exponential stability
• mean-square stability

AMS SUBJECT CLASSIFICATIONS:

• 65C30
• 65L07

Acknowledgments

The research was supported by the Natural Science Foundation of Heilongjiang Province.

Disclosure statement

No potential conflict of interest was reported by the author(s).