An analytic approximation of solutions of stochastic differential delay equations with Markovian switching

作者：Bao Jianhai^*; Hou Zhenting

来源：Mathematical and Computer Modelling, 2009, 50(9-10): 1379-1384.

DOI：10.1016/j.mcm.2009.07.006

• Taylor approximation
• Strong convergence
• Markovian switching
• Stochastic differential delay equation

In this paper, we are concerned with the stochastic differential delay equations with Markovian switching (SDDEwMSs). As stochastic differential equations with Markovian switching (SDEwMSs), most SDDEwMSs cannot be solved explicitly. Therefore, numerical solutions, such as EM method, stochastic Theta method, Split-Step Backward Euler method and Caratheodory's approximations, have become an important issue in the study of SDDEwMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEwMSs in the sense of the L(p)-norm when the drift and diffusion coefficients are Taylor approximations.

• 出版日期2009-11
• 单位中南大学