Convergence of numerical solutions to stochastic differential equations with Markovian switching

摘要

The paper develops strong approximation schemes for solutions of stochastic differential equations with Markovian switching (SDEwMSs). The convergent orders of existing strong numerical schemes all are 0.5. This paper provides a convergence theorem for the construction of strong approximations of any given order of convergence for SDEwMSs, and then constructs the order 1 scheme, the order 1.5 scheme.The paper also develops a new way to simulate the Markov chain and hence the order 1 scheme. Finally, a numerical example is provided to illustrate the theoretical results.