The Partially Truncated Euler-Maruyama Method for super-linear Stochastic Delay Differential Equations with variable delay and Markovian switching

TL;DR

This paper introduces a partially truncated Euler-Maruyama method tailored for super-linear stochastic delay differential equations with variable delay and Markovian switching, analyzing its convergence and stability.

Contribution

It develops a novel numerical method specifically designed for complex SDDEs with super-linear growth, variable delays, and Markovian switching, and studies its theoretical properties.

Findings

The method converges under generalized Khasminskii conditions.

The numerical solution maintains stability for the considered SDDEs.

The approach extends existing methods to more complex stochastic systems.

Abstract

A class of super-linear stochastic delay differential equations (SDDEs) with variable delay and Markovian switching is considered. The main aim of this paper is to develop the partially truncated Euler-Maruyama (EM) method for the super-linear SDDEs with variable delay and Markovian switching, and investigate the convergence and stability properties of the numerical solution under the generalized Khasminskii0type condition.