Potential Theory

  • Krishna B. Athreya
  • Peter E. Ney
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 196)

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.

Keywords

Assure Convolution Summing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1972

Authors and Affiliations

  • Krishna B. Athreya
    • 1
  • Peter E. Ney
    • 1
  1. 1.University of WisconsinMadisonUSA

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