Q6.

6. Let {Xt}t62l be a discrete MC, with transition matrix P. Define the reverse-time process as {Yr} E {Xt}- a) Show that {Yr} is a MC. b) Assume that {Xt} is stationary with distribution 1: (i.e., 11'(t) = It, for all t). i. Compute the transition matrix of the reverse chain {Yr} as function of P, 111'. ii. Show that the MC is reversible, i.e., the transition matrix for {Yr} is the same as for {X t}, if and only if the detailed balance equations are satisfied. c) Repeat parts a), b) for a continuous MC with generator matrix