马氏骨架过程理论在两个数学模型中的应用
【摘要】 马尔可夫骨架过程是一类较为综合的随机过程,它包含了许多随机过程,如马尔可夫过程、半马尔可夫过程、逐段决定马尔可夫过程等一系列经典的随机过程,有着重要而广泛的理论和应用价值。马尔可夫骨架过程是侯振挺等人于1997年首次提出,并在后来的研究工作中得到进一步的补充完善,广泛应用于分支过程、存储论、排队论等领域,成功地解决了排队论等问题的瞬时分布、极限分布、遍历性等经典难题,同时也提出了许多新问题和新设想。本文采用马氏骨架过程理论,特别是Doob骨架过程理论,研究再生分支过程和多类型分支过程。在模型中各个随机变量均服从一般分布的条件下,得到如下结果：一、以粒子分裂为例将经典的分支过程进行推广到再生分支过程,进而得出再生分支过程的瞬时分布和极限分布；二、以粒子分裂为例将经典的两性分支过程推广到有限维多类型分支过程,进而得出有限维多类型分支过程的瞬时分布。
硕士论文代写-【Abstract】 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.
【关键词】 分支过程； 马尔可夫骨架过程； Doob骨架过程； 瞬时分布； 极限分布； 多类型分支过程；
代写硕士论文-【Key words】 branch process； Markov skeleton process； Doob skeleton process； instantaneous distribution； limit distribution； multiple-type branch process；
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