Computer aided solving the high-order transition probability matrix of the finite Markov chain q Zhenqing Li a , Weiming Wang b, * a Laboratory of Quantitative Vegetation Ecology, Institute of Botany, The Chinese Academy of Science, Beijing 100093, China b School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China Abstract In this paper, by using theories of stochastic process and computer algebra, a reliable algorithm for computing the high-order transition probability matrix of finite Markov chain is established, a new mechanical procedure markovproc is established, too. The procedure markovproc give not only the exact expression of the Markov chains, but also the limiting probability. Some examples are presented to illustrate the implementa- tion of the algorithm. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Markov chain; Transition probability matrix; Algorithm; Mechanization; Maple 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.02.003 q The project is supported by the Natural Science Foundation of China (Grant Nos. 30270249 & 10371090). * Corresponding author. E-mail addresses: lizq@ibcas.ac.cn (Z. Li), weimingwang2003@163.com (W. Wang). Applied Mathematics and Computation xxx (2005) xxx–xxx www.elsevier.com/locate/amc ARTICLE IN PRESS