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BMAP的轨道分析和Q过程的伴随MAP
Path Analysis of BMAP and Adjoint MAP of a Q Process
本文用轨道分析方法研究批量Markov到达过程（BMAP），有别于研究BMAP常用的矩阵解析方法.通过BMAP的表现（Dk，k=0，1，2，...），得到BMAP的跳跃概率，证明了BMAP的相过程是时间齐次Markov链，求出了相过程的转移概率和密度矩阵.此外，给定一个带有限状态空间的Q过程J，其跳跃点的计数过程记为N，证明了Q过程J的伴随过程X*=（N，J）是一个MAP，求出了该MAP的转移概率和表现（D0，D1），它们是通过密度矩阵Q来表述的.
This article researches the batch Markov arrival process (BMAP) by using path-analysis method which is different from using conventional matrix analysis method. We are capable of calculating its jumping probability through the representation (Dk, k=0, 1, 2,...) of BMAP, demonstrating the fact that BMAP's phase process is time-homogeneous Markov chain, figuring out the transition probabilities and density matrix of the phase process. Moreover, if we give a Q process J with a finite state space and define the counting process of its jumping points as N, we can demonstrate that adjoint process X*=(N, J) of Q process J is a MAP. The MAP's transition probabilities and representation (D0, D1) are exactly worked out, which are expressed by density matrix Q.
批量Markov到达过程(BMAP) / Markov到达过程(MAP) / 轨道分析 / Q过程 / 伴随过程 {{custom_keyword}} /
batch Markov arrival process (BMAP) / Markov arrival process (MAP) / path analysis / Q process / adjoint process {{custom_keyword}} /
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国家自然科学基金项目（11671132，11601147）；湖南省哲学社会科学基金项目（16YBA053）；湖南省教育厅科研基金重点项目（15A032）
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