马尔可夫链的市场经济分析

目 录

摘 要 1

Abstract 2

前 言 3

１ 绪论 4

1.1 马尔可夫过程的历史 4

1.2 马尔可夫过程的直观背景 5

1.3 马尔可夫链在我国目前的研究现状 6

２ 马尔可夫链 7

2.1 马尔可夫链的定义 7

2.2 马尔可夫链的几个重要性质 9

３ 马尔可夫链的市场预测方法研究 11

3.1 马尔可夫链对市场占有率的预测 11

3.1.1 应用马尔可夫链理论研究市场占有率的前提条件 113.1.3 市场占有率矩阵的预侧值 12

3.2 转移概率矩阵的调整 15

3.3 公司期望利润预测 18

４ 总结 21

参考文献 22

致谢 23

摘 要

马氏链运用数学模型对定性问题进行预测提供了1种思路，丰富了预测的内容。运用马氏链进行预测的基本思路是：首先，把现象看作是1种系统，并对该系统进行科学的状态划分。根据系统的实际和需要划分多个状态，系统所划分出来的各个状态就是要预测的内容。其次，对现象各种状态的状态概率进行统计测定，也就是判定出系统当前处于什么状态。第3，对各系统未来发展的每次转移概率进行预测，就是要确定出系统是如何转移的。最后，根据系统当前的各种状态和转移概率矩阵，推测出系统经过若干次转移后，到达各个状态的概率。本文简述了马尔可夫链的基本原理，基于经济活动的复杂，多变性及带有许多随机因素的特点，利用了马氏过程的基本特征，巧妙的构造转移概率矩阵，建立起马尔可夫预测模型，对商品市场经济的发展和公司的期望利润作出了预测。

关键词：马尔可夫链; 转移概率矩阵; 市场占有率; 期望利润

Abstract

The Markov chain carried on the forecast using the mathematical model to the qualitative question to provide one kind of mentality, has enriched the forecast content. Carries on the forecast using the Markov chain the basic mentality is: First, regards as the phenomenon is one kind of system, and carries on the science to this system the condition division. The content and needs to divide many conditions which according to the system reality, the system divides each condition which is needs to forecast. Next, carries on the statistical determination to the phenomenon each condition probability of state, also is determines the system currently to be at any condition. Third, each time transition probability which future develops to various systems carries on the forecast, is must determine how the system is shifts. Finally, according to the system current each condition and the transition probability matrix, after extrapolated the system passes through certain shifts, arrives each condition the probability. This article has summarized the Markov chain basic principle, based on economic activity complex, the polytropy and has many random factors characteristics, has used the Markov process basic characteristic, The ingenious structure transition probability matrix, establishes the Markov forecast model, has made the forecast to the commodity market economy development and companys expectation profit.

Keywords：Markov chain; Transition probability matrix; Market share; expectation profit