本文選題：馬爾可夫骨架過程 + 持有資金量��； 參考：《中南大學》2007年碩士論文

【摘要】： 馬爾可夫骨架過程是一類較為綜合的隨機過程,它包含了許多已有的隨機過程模型,如馬爾可夫過程、半馬爾可夫過程、逐段決定的馬爾可夫過程等一系列的經(jīng)典的隨機過程,具有重要的理論和應用價值。1997年,侯振挺教授等人首次提出馬爾可夫骨架過程,并且將其應用于排隊論、控制論等領域,成功地解決了排隊論的瞬時分布、平穩(wěn)分布、遍歷性等一系列的經(jīng)典難題,并且提出了許多新問題和新思想。 本文主要是利用馬爾可夫骨架過程理論來研究消費經(jīng)濟學的微觀數(shù)學模型,給出了消費系統(tǒng)的持有資金量L(t)的統(tǒng)計規(guī)律,研究了消費系統(tǒng)的收入時間間隔和支出時間間隔均服從一般分布時持有資金L(t)的瞬時分布,給出了一種無債消費系統(tǒng)的持有資金量L(t)的瞬時分布及平穩(wěn)分布。 本文的主要結(jié)果有: 第一、利用馬爾可夫骨架過程法列出了在任何時刻t消費系統(tǒng)持有的資金量的瞬時分布及其所滿足的線性積分方程,并證明其概率分布是該方程的最小非負解。 第二、作為特殊情況給出了一種無債消費系統(tǒng)持有的資金量的瞬時分布及平穩(wěn)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.
【學位授予單位】：中南大學
【學位級別】：碩士
【學位授予年份】：2007
【分類號】：F224;F014.5

【引證文獻】

相關(guān)碩士學位論文 前1條

1 張振良;大學生消費狀況的社會學分析[D];華中科技大學;2009年

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本文編號：1887317