Poisson Processes

  • V. G. KulkarniEmail author
Part of the Springer Texts in Statistics book series (STS)


In the previous chapter, we studied a discrete-time stochastic process {X n, n ≥ 0} on finite state space with Markov property at times n = 0, 1, 2 ···. Now we would like to study a continuous-time stochastic process {X(t), t ≥ 0} on a finite state space with Markov property at each time t ≥ 0. We shall call such a process continuous-time Markov Chain (CTMC). We shall see in the next chapter that a finite-state CTMC spends an exponentially distributed amount of time in a given state before jumping out of it. Thus exponential distributions play an important role in CTMCs. In addition, the Poisson distribution and Poisson processes also form the foundation of many CTMC models. Hence we study these topics in this chapter.


Poisson Process Computational Problem Compound Poisson Process Exponential Random Variable Poisson Random Variable 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of North CarolinaChapel HillUSA

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