Approximate solutions of stochastic differential delay equations with Markovian switching

Our main aim is to develop the existence theory for the solutions to stochastic dierential delay equations with Markovian switching (SDDEwMSs) and to establish the convergence theory for the Euler{Maruyama approximate solutions under the local Lipschitz condition. As an application, our results are used to discuss a stochastic delay population system with Markovian switching