随机环境中的泊松过程

Poisson Process in the Random Environment

引进了随机环境中的泊松过程模型,推导出其转移概率,讨论了该过程与均匀分布和Γ分布之间的特殊关系,证明了当环境过程为坐标过程时随机环境中泊松过程是一类特殊的随机环境中马氏过程,并给出了该过程的随机Kolmogorov方程.

This article introduces Poisson process model in the random environment, deduces its transition probability, and discusses the relationships among the process as well as the uniform distribution and Γ distribution. It is proved that the Poisson process in the random environment is a special kind of Markov process in the random environment when the environment process is coordinate process. Finally, the paper gives the random Kolmogorov equation of this process.