FINITE-STATE MARKOV CHAINS - MIT OpenCourseWare

Chapter 3 FINITE-STATE MARKOV CHAINS 3.1 Introduction The counting processes {N(t); t > 0} described in Section 2.1.1 have the property that N(t) changes at discrete instants of time, but is defined for all real t > 0. The Markov chains to be discussed in this chapter are stochastic processes defined only at integer values of time, n = 0, 1,....At each integer time n ≥ 0, there is an ...

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Since the state space is countable (or even finite) it customary (but not always the case) to use the integers Z or a subset such as Z + (non-negative integers), the natural numbers N = {1,2,3,···} or {0,1,2,··· ,m} as the state space. The specific Markov chain under consideration often determines the natural notation for the state space.

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2 1MarkovChains 1.1 Introduction This section introduces Markov chains and describes a few examples. A discrete-time stochastic process {X n: n ≥ 0} on a countable set S is a collection of S-valued random variables defined on a probability space (Ω,F,P).The Pis a probability measure on a family of events F (a σ-field) in an event-space Ω.1 The set Sis the state space of the process, and the

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