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A Closed Form Probability Mass Function for Occupation Times in a Three-State Markov Chain
Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA
Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA
- 1 Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA
- 2 Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA
Advances in Pure Mathematics·Volume 15 (2025)·Pages 554–561·Published 8 August 2025·DOI10.4236/apm.2025.158029
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Abstract
We obtain a closed form expression for the joint probability mass function of the occupation times for a Three-State Markov chain. Our representation extends the long-standing result for a Two-State Markov chain by utilizing the method of probability generating functions given in Pedler.
KeywordsOccupation TimesMarkov ChainsProbability Generating FunctionsProbability Mass Function
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