建立消费经济学微观数学模型的马尔可夫骨架过程方法

发布时间：2018-05-14 09:33

本文选题：马尔可夫骨架过程 + 持有资金量　；参考：《中南大学》2007年硕士论文

【摘要】： 马尔可夫骨架过程是一类较为综合的随机过程,它包含了许多已有的随机过程模型,如马尔可夫过程、半马尔可夫过程、逐段决定的马尔可夫过程等一系列的经典的随机过程,具有重要的理论和应用价值。1997年,侯振挺教授等人首次提出马尔可夫骨架过程,并且将其应用于排队论、控制论等领域,成功地解决了排队论的瞬时分布、平稳分布、遍历性等一系列的经典难题,并且提出了许多新问题和新思想。本文主要是利用马尔可夫骨架过程理论来研究消费经济学的微观数学模型,给出了消费系统的持有资金量L(t)的统计规律,研究了消费系统的收入时间间隔和支出时间间隔均服从一般分布时持有资金L(t)的瞬时分布,给出了一种无债消费系统的持有资金量L(t)的瞬时分布及平稳分布。本文的主要结果有: 第一、利用马尔可夫骨架过程法列出了在任何时刻t消费系统持有的资金量的瞬时分布及其所满足的线性积分方程,并证明其概率分布是该方程的最小非负解。第二、作为特殊情况给出了一种无债消费系统持有的资金量的瞬时分布及平稳分布。
[Abstract]:Markov skeleton process is a kind of synthetic stochastic process. It contains many existing stochastic process models, such as Markov process, semi-Markov process, piecewise decision Markov process and so on. In 1997, Professor Hou Zhenting and others first proposed Markov skeleton process, and applied it to queuing theory, cybernetics and other fields, successfully solved the instantaneous distribution and stationary distribution of queuing theory. Ergodicity and so on a series of classical problems, and put forward many new problems and new ideas. In this paper, we mainly use Markov skeleton process theory to study the microscopic mathematical model of consumer economics, and give the statistical law of the amount of money held in the consumption system. This paper studies the instantaneous distribution of the income time interval and the expenditure time interval from the general distribution to the holding capital Lt), and gives the instantaneous distribution and the stationary distribution of the holding capital of a kind of debt free consumption system. The main results of this paper are as follows: First, by using Markov skeleton process method, the instantaneous distribution of the amount of funds held by t consumption system at any time and its satisfying linear integral equation are given, and it is proved that its probability distribution is the least nonnegative solution of the equation. Secondly, as a special case, the instantaneous and stationary distribution of the amount of funds held by a debt-free consumption system is given.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2007
【分类号】：F224;F014.5

【引证文献】