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Poisson Processes

  • V. G. KulkarniEmail author
Chapter
  • 10k Downloads
Part of the Springer Texts in Statistics book series (STS)

Abstract

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.

Keywords

Poisson Process Computational Problem Compound Poisson Process Exponential Random Variable Poisson Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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