The number of visits to a subset of the state space by a discrete- parameter semi-Markov process (Q1344834)
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scientific article; zbMATH DE number 724096
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The number of visits to a subset of the state space by a discrete- parameter semi-Markov process |
scientific article; zbMATH DE number 724096 |
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The number of visits to a subset of the state space by a discrete- parameter semi-Markov process (English)
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22 February 1995
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A discrete-parameter irreducible semi-Markov process with a finite state space is considered. The state space is the union of two disjoint nonempty subsets \(A_1\) and \(A_2\). The distribution of a random number of transitions \(A_1 \to A_2\) during the first \(t + 1\) time instants \((t \geq 1)\) is investigated. A compact formula for this distribution in terms of the semi-Markov transition function is derived.
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counting process
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closed form expression
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semi-Markov process
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