Question

(5) Consider the Markov chain with infinite state space {1, 2, 3, ...} and transi-tion matrix given by p(i, i + 2) = q and p(i, max{1, i – 1})

= 1- q for i>=1. For which values of q E [0, 1] is this chain transient, positive recurrent, and null recurrent?

Fig: 1

Fig: 2

Fig: 3