Be S = {1, 2, 3, 4} and the stochastic matrix P:
Suppose X0 = 3. Find the number of moves expected from there until it is observed the 123 pattern for the first time.
I know if I find the invariant distribution, I can find the return time to state 3 by the equation m=d/π3 , where d is the period of the chain, but how do i find the expected time for a specific path? and in this case it seems that it has no invariant distribution (I may be making mistakes in the calculations)
Suppose X0 = 3. Find the number of moves expected from there until it is observed the 123 pattern for the first time.
I know if I find the invariant distribution, I can find the return time to state 3 by the equation m=d/π3 , where d is the period of the chain, but how do i find the expected time for a specific path? and in this case it seems that it has no invariant distribution (I may be making mistakes in the calculations)
