mc4n - Winter 2010 Pstat160a Hand-out MC # 4 Mean time in...

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Winter 2010 Pstat160a Hand-out MC # 4 Mean time in transient states and applications 1) Markov Chains with transient states Start with a transition matrix P for a finite Markov chain with some transient and recurrent states (recall cannot have only transient states). Extract from P a new matrix P T that involve only transient states. Note that the sum of at least one of the row is < 1 now (otherwise the chain cannot leave the class and so the class would be recurrent). For example the first matrix from handout Markov chains 2, we found that 1,2,3 are transient, 4,5 are recurrent. P = . 3 . 6 0 0 . 1 0 . 4 . 6 0 0 . 4 . 6 0 0 0 0 0 0 . 4 . 6 0 0 0 1 0 P T = . 3 . 6 0 0 . 4 . 6 . 4 . 6 0 Let S the matrix with entries s ij = expected number of visit to j , starting at i Then S = ( I - P T ) - 1 where I = 1 0 0 0 .... 0 1 0 0 ... ........ ... 0 0 0
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This note was uploaded on 01/10/2011 for the course STAT 160A taught by Professor Bonnet during the Winter '10 term at UCSB.

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mc4n - Winter 2010 Pstat160a Hand-out MC # 4 Mean time in...

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