Asian Journal of Probability and Statistics

Existence and Uniqueness of Stationary Probability Vector for Stochastic Matrices using Farkas’ Lemma

Somdeb Lahiri *

PDE University and Adjunct Professor LJ University, Ahmedabad, India.

*Author to whom correspondence should be addressed.

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Abstract

The purpose of this note is to provide a simple proof of existence of stationary probability vectors (fixed points) for stochastic matrices using Farkas’ lemma. This result as well as the uniqueness of stationary probability vectors also holds for a certain subclass of quasi-stochastic matrices.

Keywords: Farkas’ lemma, stochastic matrices, stationary probability

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