Determine the asymptotic state probability vector

Question

Assignment:

1. Determine the asymptotic state probability vector of the MC with infinitesimal generator matrix

2. Consider a BDP with state space S = {0, 1} and transition intensities

q0,1= λ q1,0= μ

Determine what follows.

a) The transition probabilities P_i,j(h) in a very short time interval of duration h.

b) The asymptotic state probability vector π.

3. Consider a BDP with birth rates equal to

and death rates

where K is a positive integer that represents the maximum size of the population. Determine the asymptotic state probability vector.