Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching

Abstract

Abstract In this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type condition.

Keywords

• Partially truncated Euler–Maruyama method
• Neutral stochastic differential delay equations
• Markovian switching
• Highly nonlinear and nonautonomous equations