Development of numerical methods for nonlinear hybrid stochastic functional differential equations with infinite delay
Guozhen Li, Xiaoyue Li, Xuerong Mao
Published: 2025/8/30
Abstract
This paper focuses on explicit numerical approximations for nonlinear hybrid stochastic functional differential equations with infinite delay. Precisely, explicit truncated Euler-Maruyama schemes are proposed, $2p$th $(p \ge 1)$ moment boundedness and strong convergence of the numerical solutions are obtained. Under slightly stronger conditions, the $1/2$ order convergence rate is established. Furthermore, the exponential stability, including moment and almost sure exponential stability, is examined. Finally, an example is provided to illustrate our results.