The Theory Of Markov Skeleton Processes And The Application Of Two Mathematical Models

Markov skeleton process is a kind of comparatively comprehensive stochastic process.It contains a lot of classical stochastic models, such as the Markov process,Semi-Markov process and Markov decision process.It has a wide range of important theories and practical values.Markov skeleton process is proposed by professor Hou zhenting for the first time in 1997 and has been perfected in subsequent research.It is widely used in many fields,such as branching processes, stored theory, queuing theory and so on. It has successfully resolved many classical problems such as instantaneous distribution,limiting distribution, ergodicity in queuing theory. A number of new issues are proposed at the same time.In this paper, we mainly study the regeneration branching processes and finite-dimensional branching processes by the theory of Markov skeleton process, especially the theory of Doob skeleton process.As the models are all satisfied the normal distribution, We obtain the following results:First, we just take the particle split as an example to promote the classical branch process to the regeneration branch process.Then we get the instantaneous distribution and the limit distribution of the regeneration branch process. Second, we just take the particle split as an example to promote the classical amphoteric branch process to the finite-dimensional multi-type branch process. Then we get the instantaneous distribution of the finite-dimensional branching process.