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Transition and Generator matrix

You can create a probability transition matrix P from a transition rate matrix Q, but not vice versa.

Think about it like this: if you know the average speed of two runners you can work out the probability of who will win a race. But if you know the probability of who will win, you don’t know how fast they are going (only how fast relative to one another).

I am reasonably confident the notes cover the method of generating a P matrix from a Q matrix, but I don’t have a copy so can’t be sure. It’s a very common question / natural thing to do given a Q matrix.
 
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