Question: Consider a Markov chain with transition probability matrix P., and sup- pose that P, increases in i for all k. (a) Show that, for all

Consider a Markov chain with transition probability matrix P., and sup- pose that P, increases in i for all k.

(a) Show that, for all increasing functions

f, , P.,f(j) increases in i.

(b) Show that P, increases in i for all k, where P", are the n-step transition probabilities, n 2.

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