Question

Got stuck on this problem for several hours, literally in a desperate situation, sincerely could any expert give a help? Many many thanks in advance!!

Problem 4 (20p). Let p є 10, il with p , and let (Xn)n-0 be the Markov chain on Z with initial distribution 0 and transition matrix 11 : Z x Z O, j given by 1-p if y-r- 1 otherwise Use the strong law of large numbers to show that each state is transient. Hint: consider another Markov chain with additional structure but with the same distribution and transition matrix

Answer 1

itenthot Sine state spate setisinfini te n: denote the State spate at nthtme gues thestate aten ti icin "tdEN, then at the nest stae the chainftot

He nce, yn : Co +2.7; 12 2. 0,5. tnd'n ให้1.mystie?'4fnįteujoitt. Yn vente he tai usher ene all the stete e chainabe tonset.

Note: zi is a 9andomaiable follous Beou cp and zi state space Cs el of integes) Suppose at any stage the chain is al x. Thev yp aofn ?e hevd ocus cain will yth state ondft tail ocueos caîn xth tate.