Potential Theory

Abstract

If P = {P(i,j); i,j =0,1,2,...,} is the transition function of any stationary Markov chain, then {η _i ; i=0,1,...} is called a stationary or invariant measure for P if η _i ≥0 and

$$ {\eta _j} = \sum\limits_{i = 0}^\infty {{\eta _i}P(i,j),} \;j \geqslant 0. $$

(1)

If in addition Ση _i <∞ (or without loss of generality, if Ση _i =1), then {η _i } is a stationary distribution.