A generator for a continuous time Markov process X(t) is given by G= -X 0 12/11 - 1 / 1 0 1 - The states are {1,2,3}, so

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A Generator For A Continuous Time Markov Process X T Is Given By G X 0 12 11 1 1 0 1 The States Are 1 2 3 So 1 (50.1 KiB) Viewed 22 times

A generator for a continuous time Markov process X(t) is given by G= -X 0 12/11 - 1 / 1 0 1 - The states are {1,2,3}, so e.g. 912 = 1 and 923 = }, etc. (i) Write down the probabilities of moving from one state to another state after the length of stay in a particular state is complete. (ii) Show that lim h-0 P(X(t + h) = 3 X (t) = 1) h → 0 as h→0. (iii) The stationary probability vector 7 satisfies a P(t) = 7 for all t, where P(t) is the matrix of probabilities given by Pij(t) = P(X(t) = ||X(0) = i). Find 7 and show that a G = 0. = (iv) At time t = 2 the process is in state 1; how much longer does it stay in this state. (v) Given X (0) = 1, find the probability that the process has not visited state 3 by time t = 4.