Let (left(X_{n} ight)) be a Markov chain with the transition matrix below. Show that the constant function

Let \(\left(X_{n}\right)\) be a Markov chain with the transition matrix below. Show that the constant function \(f=2\) is excessive (i.e., \(f \geqslant T \cdot f\) ). More generally, show that for an arbitrary Markov chain with finite state space, the constant function \(f=c\) is excessive.

Transcribed Image Text:

1/2 1/2 0 T=1/3 1/3 1/3 1/4 0 3/4.