Lecture 12

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Unformatted text preview: ch i: A Markov chain is called temporally homogeneous if : PrfAn = j jAn,1 = ig = PrfAn+m = j jAn+m,1 = ig: The transition probability is then denoted by pij . For all possible values of i j , one can denote he the transition probability as a matrix with elements pij . The transition in n-step is given by pij n = PrfAn = j jA0 = ig: Since a Markov chain has stationary transition probabilities, we have pij n = PrfAm+n = j jAm = ig for all m  0 and n 0: 3. Continuous-time, Markov Chain Let fX t 0  t 1g be a Markov process with countable state space S = f0 1 2 :::g over continuous time-space t. For, example, X t can be the number of customers in the system at time t. For continuous time, discrete space (Markov chains) the transition probability is denoted by, pij t = Prfxt + u = j jxu = ig t 0 i j 2 S X pij t = 1 Note, j Now, we can consider all the possible cases for i in matrix notation, P t := pij t := CS 522, v 0.94, d.medhi, W’99 for each i: j at time t giving us a matrix of information. Thus, transition...
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This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.

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