The Stationary Distribution for Blackwell’s Markov Chain

I find the stationary distribution for the Markov process given by D.Blackwell in Blackwell (Ann Math Statist 29:313–316 1958). This process has countably many states all of which are instantaneous. The stationary distribution for a Markov chain, both in continuous and discrete time, composed of a finite number of mutually independent, two-state Markov chains, is also derived. Additionally, I give a compact formula for the entropy associated with these invariant distributions.

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Publication Details

Journal
Methodology And Computing In Applied Probability
Published
2025-09-01
DOI
https://doi.org/10.1007/s11009-025-10202-5
Primary Topic
Data Management and Algorithms
Type
article
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article

The Stationary Distribution for Blackwell’s Markov Chain

Ernest Nieznaj
Methodology And Computing In Applied Probability
Data Management and Algorithms
article

The Stationary Distribution for Blackwell’s Markov Chain

Ernest Nieznaj
article en

Abstract

I find the stationary distribution for the Markov process given by D.Blackwell in Blackwell (Ann Math Statist 29:313–316 1958). This process has countably many states all of which are instantaneous. The stationary distribution for a Markov chain, both in continuous and discrete time, composed of a finite number of mutually independent, two-state Markov chains, is also derived. Additionally, I give a compact formula for the entropy associated with these invariant distributions.

Methodology And Computing In Applied ProbabilityVol. 27(3)
Lublin University of Technology (PL)
Openalex Percentile: Top 71%
Data Management and Algorithms
DOIOpen Access PDFOpenAlex
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The Stationary Distribution for Blackwell’s Markov Chain — Ernest Nieznaj · Methodology And Computing In Applied Probability (2025) | TGRS Research Map | TGRS