ScholarLens Back to search
1974•Advances in Applied ProbabilityRequires access

Periodicity in Markov renewal theory

Erhan Çınlar

Open publisher page 27 citations

Abstract

In an irreducible Markov renewal process either all states are periodic or none are. In the former case they all have the same period. Periodicity and the period can be determined by direct inspection from the semi-Markov kernel defining the process. The periodicity considerably increases the complexity of the limits in Markov renewal theory especially for transient initial states. Two Markov renewal limit theorems will be given with particular attention to the roles of periodicity and transient states. The results are applied to semi-Markov and semi-regenerative processes.

About this research paper

What this paper is about

In an irreducible Markov renewal process either all states are periodic or none are. In the former case they all have the same period. Periodicity and the period can be determined by direct inspection from the semi-Markov kernel defining the process. The periodicity considerably increases the complexity of the limits in Markov renewal theory especially for transient initial states. Two Markov renewal limit theorems will be given with particular attention to the roles of periodicity and transient states. The results are applied to semi-Markov and semi-regenerative processes.

Why it matters

OpenAlex reports 27 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In an irreducible Markov renewal process either all states are periodic or none are. In the former case they all have the same period. Periodicity and the period can be determined by direct inspection from the semi-Markov kernel defining the process. The periodicity considerably increases the complexity of the limits in Markov renewal theory especially for transient initial states. Two Markov renewal limit theorems will be given with particular attention to the roles of periodicity and transient states. The results are applied to semi-Markov and semi-regenerative processes.

Key concepts: Markov renewal process, Mathematics, Markov chain, Markov kernel, Renewal theory, Markov process, Markov model, Limit (mathematics)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Periodicity in Markov renewal theory — Research Paper | ScholarLens