The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching

Abstract

Abstract In this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.

Keywords

• Stochastic θ method
• SDEs with Markovian switching
• Numerical solutions
• Stationary distribution