Consumer Economics Microscopic Mathematical Model Markov Skeleton Process Approach

Markov skeleton process is a new type of stochastic process and containing many classical processes such as Markov process, semi-Markov process, piecewise deterministic Markov process. It is very important in theory and application. In 1997, Prof. Hou Zhenting and his colleagues raised this kind of process and applied it to fields in queue theory and cybernetics and solved many difficult queuing theory problems such as transient distribution, stationary distribution and ergodicity successfully.By applying the theory of Markov skeleton process, this paper mainly studies the micro mathematics model of consumer economics, presents the statistical rules of holding the amount of funds in consumption system, studies the transient distribution of holding funds when both income time intervals and expense time intervals are satisfied with regular distribution, and presents a transient distribution and stationary distribution of holding funds in no debt consumption system.In this dissertation, we drew the following conclusions:Firstly, applying the Markov skeleton process method, we can get the transient distribution of holding funds in consumption system in any time and the satisfied linear integral equations .we can also prove that the probability distribution is the minimal nonnegative solution of the equation.Secondly, we present a transient distribution and stationary distribution of holding funds in no debt consumption system as a special case.