Poisson Processes

Abstract

AbstractIn 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.KeywordsPoisson ProcessComputational ProblemCompound Poisson ProcessExponential Random VariablePoisson Random VariableThese 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.