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

Somdeb Lahiri

doi:10.9734/ajpas/2022/v20i4442

Research Article Open access CC BY 4.0

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

Somdeb Lahiri

Asian Journal of Probability and Statistics · pp. 94–99 · Published 8 Dec 2022

10.9734/ajpas/2022/v20i4442

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.

Farkas’ lemma stochastic matrices stationary probability

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Somdeb Lahiri (2022). Existence and Uniqueness of Stationary Probability Vector for Stochastic Matrices using Farkas’ Lemma. Asian Journal of Probability and Statistics , 94–99. https://doi.org/10.9734/ajpas/2022/v20i4442

Affiliations

Somdeb Lahiri — PDE University and Adjunct Professor LJ University, Ahmedabad, India.

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