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Question from my Spring 2008 STAT 333 exam
Consider a continuoustime 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 offdiagonals 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.
 Spring '08
 Chisholm

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