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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

Markov Chain Harmonic Function Stationary Measure Green Function Potential Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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