STAT444 Lecture Notes - River Irk
11 Mar 2019
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If a proposition state space then it is recurrent irreducible mc has a finite of proof the mc is transient then with probability idea if each. Finite the states the mc has no where to go after that time contradiction last visit last visit time for all time state has states a. Remark we can actually prove that chain must be positive rec and the mc is irreducible the markov if the state space is finite. Theorem periodicity is a class property i c j di dj. For an irreducible mc its period is defined as the period of any state limiting distribution. In this part we are interested in and ne plxn i. To make things simple we focus on the irreducible case. Basic limit theorem be an irreducible aperiodic positive unique stationary distribution a exists moreover. Lethn n od recurrent dnc then ko ti austin. Distribution dependent where start got on we limiting distribution.
