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The point process of state transitions in a regular Markov chain

The point process of state transitions in a regular Markov chain In this paper, we study the point process of state transitions in a regular Markov chain. Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition frequency, the absorbing distribution, the renewal distribution and the entering probability. As an application, using these formulas we derive the LS transform of the busy period for theM/M/∞ queue. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The point process of state transitions in a regular Markov chain

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Publisher
Springer Journals
Copyright
Copyright © 1998 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02683821
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the point process of state transitions in a regular Markov chain. Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition frequency, the absorbing distribution, the renewal distribution and the entering probability. As an application, using these formulas we derive the LS transform of the busy period for theM/M/∞ queue.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 4, 2007

References