马尔可夫调制的随机时滞微分方程解的算法分析  

An Algorithmic Analysis of Solutions of Stochastic Differential Delay Equations with Markovian Switching

作　　者：刘德志[1] 杨桂元[1] 鲍建海[2] 张伟[1] 

机构地区：[1]安徽财经大学统计与应用数学学院,安徽蚌埠233030 [2]广西工学院信息与计算机科学系,广西柳州545000

出　　处：《菏泽学院学报》2008年第2期10-13,23,共5页Journal of Heze University

基　　金：安微省教育厅自然科学基金资助项目(KJ2008B011)

摘　　要：一般地,对于马尔可夫调制的随机时滞微分系统来说,很难求出其精确解.即使近似解被求出来,因为其复杂的原因也不方便使用.因此,很多数学家引入了很多方法,例如:EM逼近、离散近似逼近、随机泰勒展式等等.由于近似方法不同而有不同的收敛速度.主要研究当漂移系数和扩散系数满足随机泰勒展式时近似解的收敛速度,得出优于EM逼近的方法.In this paper, we are concerned with the neutral stochastic differential delay equations with Markovian switching. In general it is not impossible to find explicitly the solution for stochastic differential delay equations with Markovian switching. Even when such a solution can be found, it may be only in implicit form or too complicated to visualize and evaluate numerically. Therefore, many approximate schemes represented, for example, EM scheme, time discrete approximations, stochastic Taylor expansion, and so forth. Meanwhile, the rate of approximation to the true solution by the numerical solution is different for different numerical schemes. The aim of this paper shows that the rate of approximation between the true solution and numerical solution is faster than EM method in the sense of the norm when the drift and diffusion coefficients are Taylor approximations.

关 键 词：泰勒近似 收敛速度 马尔可夫链 随机 

分 类 号：O211.63[理学—概率论与数理统计]