Numerical Approximation Of Steady-state Distribution Of Stochastic Differential Equations With Markov Switching

In this paper,we study the stationary distribution of stochastic differential equations(SDEs)with Markovian switching.Since it is difficult to obtain the stationary distribution of the exact solutions,we need to use a class of numerical methods to obtain the numerical stationary distribution,which are used to approximate those of the underlying equations.Firstly we give some basic theorems,formulas and review existing literatures.Then we discuss SDEs with Markovian switching in two cases.In the first case,each equation in the switching system has a unique stationary distribution and in the second case,some equations do not have the stationary distribution.In particular,we use the ? method when we discuss the stationary distribution of numerical solutions.When ? ? [0,1/2),both of the drift and diffusion coefficients satisfy the global Lipschitz condition.When? ? [1/2,1],the drift coefficient only satisfies the one-side Lipschitz condition,and the diffusion coefficient satisfies the global Lipschitz condition.Finally,numerical examples of one-dimensional and two-dimensional equations are given to illustrate the theoretical results.