一类受Poisson干扰的Markov过程应跳性逼近

计算物理 ›› 1998, Vol. 15 ›› Issue (2): 199-204.

一类受Poisson干扰的Markov过程应跳性逼近

李镇华¹, 吴声昌², 刘小清^1,2

1. 香港城市大学数学系;
2. 中国科学院应用数学研究所, 管理、决策与信息系统开放实验室, 北京 100080

收稿日期:1996-10-14 修回日期:1997-10-31 出版日期:1998-03-25 发布日期:1998-03-25
作者简介:李镇华,男,41,助理教授,博士,香港城市大学数学系

Jump-Adapted Approximation of a Class of Poisson Driven Markov Processes

Li Zhenhua¹, Wu Shengchang², Liu Xiaoqing^1,2

1. Department of Mathematics, City University of Hong Kong 83 Tat Chee Avenue, Kowloon, Hong Kong;
2. Institute of Applied Mathematics, Academia Sinica Laboratory of Management Decision and In formation Systems, Beijing 100080

Received:1996-10-14 Revised:1997-10-31 Online:1998-03-25 Published:1998-03-25

摘要/Abstract

摘要： 对于随机微分方程约束下受Poison干扰的Markov过程,给出了一种具有应跳性的轨道逼近方法:将每条轨道分解为若干连续阶段,在每个阶段中建立了相应的常微分方程,并采用Runge-Kuta方法求解。该方法已用于研究Langevin方程和Dufing-VanderPol振子。

关键词: 随机微分方程, 数值近似, Poisson过程

Abstract: This paper presents a pathwisely jump-adapted approximation of the Poisson driven Markov processes governed by stochastic differential equations.Any trajectory of the processes is divided into continuous phases. Within each phase, the corresponding ODEs are established and solved by the Runge Kutta schemes.The method is applied to investigate the Langevin equation as well as the Duffing-Van der Poloscillator.

Key words: Poisson processes, stochastic differential equations, jump-adapted approximation, Langevin equation, Duffing-Van der poloscillator

中图分类号:

O241.8

李镇华, 吴声昌, 刘小清. 一类受Poisson干扰的Markov过程应跳性逼近[J]. 计算物理, 1998, 15(2): 199-204.

Li Zhenhua, Wu Shengchang, Liu Xiaoqing. Jump-Adapted Approximation of a Class of Poisson Driven Markov Processes[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 15(2): 199-204.

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