Convergence of numerical solution to stochastic delay differential equation with Poisson jump and Markovian switching

The main purpose of this paper is to study the convergence of numerical solutions to a class of stochastic delay differential equations with Poisson jump and Markovian switching. A numerical approximation scheme is proposed to approximate the solution to stochastic delay differential equations with Poisson jump and Markovian switching. It is proved that the Euler approximation solution converge to the analytic solution in probability under weaker conditions. Some known results are generalized and improved. An example is provided to illustrate our theory.