Question: 13.9 Consider a Markov process with state space S = {0, 1, 2,... } and transition rates qi,i+1 = ai , qi,0 = b, and

13.9 Consider a Markov process with state space S = {0, 1, 2,... } and transition rates qi,i+1 = ai

, qi,0 =

b, and qi,k = 0 in all other cases. Show the following:

a) When a > 1, this process is not regular.

b) Find the stationary distribution when a ≤ 1 and b > 0.

c) Show that the stationary distribution does not exist when a > 0 and b = 0.

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