Question_from_my_Spring_2008_STAT_333_ex

Question_from_my_Spring_2008_STAT_333_ex - Question from my...

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Question from my Spring 2008 STAT 333 exam Consider a continuous-time Markov Chain with state space S = {1, 2, 3}. The amount of time spent in state i before jumping is exponentially distributed with rate i , and given that a transition occurs, the instantaneous transition probabilities are given by P ij = 22 ij i  . a) Find the generator matrix Q for this chain. First of all, we can write out the instantaneous transition matrix P to see what it looks like: ? = ± ± ² 0 1 3 2 3 1 2 0 1 2 2 3 1 3 0 ³ ´ ´ µ We know the diagonal elements of Q are the negatives of the rates, and the off-diagonals are the rate * Pij. So:
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This note was uploaded on 12/12/2010 for the course STAT 333 taught by Professor Chisholm during the Spring '08 term at Waterloo.

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