马尔科夫调制Fokker-Planck方程Milstein方法的收敛性和稳定性  

The convergence and stability of Milstein method for Fokker-Planck equation with Markovian switching

作　　者：高玉敏[1] 丁效华[1] 

机构地区：[1]哈尔滨工业大学(威海)数学系,威海264209

出　　处：《黑龙江大学自然科学学报》2011年第1期22-27,共6页Journal of Natural Science of Heilongjiang University

基　　金：哈尔滨工业大学理学基金资助项目(HITC-200713)

摘　　要：考虑一类马尔科夫调制的Fokker-Planck方程,研究Milstein方法在均方意义下的收敛性和稳定性。证明Milstein方法的收敛阶为1/2,并且给出数值解均方稳定的条件和步长限制表达式。数值实验进一步验证了结论的正确性。Some Fokker-Planck equations with Markovian switching are considered. In the mean square sense, the convergence and stability of the Milstein method for the equations are studied. It is proved that the Milstein method is convergent with order 1/2. In addition, the conditions of stability and stepsize restriction are obtained. Finally, some numerical experiments confirm the conclusions that are gotten.

关 键 词：马尔科夫调制的Fokker-Planck方程 MILSTEIN方法 收敛性 稳定性 

分 类 号：O175.12[理学—数学]