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

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.