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An Infinite Series Expression for the Joint Probability Density Function of OccupationTimes 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 718–725·Published 3 November 2025·DOI10.4236/apm.2025.1511038
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Abstract
We obtain an infinite series expression for the joint probability density function of occupation times in a Three-State Markov chain. By extending the identity given by Darroch, we demonstrate that Pedler’s technique of employing moment generating functions can be applied to the three-state case as well.
KeywordsOccupation TimesMarkov ChainsMoment Generating FunctionsProbability Density Function
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