Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-25T03:09:14.788Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of transition probabilities in a multiparticle semi-Markov system

Published online by Cambridge University Press:  14 July 2016

David Burman
David Burman*
Affiliation:
Bell Telephone Laboratories, Holmdel, New Jersey
Get access Rights & Permissions [Opens in a new window]

Abstract

Particles enter a finite-state system and move according to independent sample paths from a semi-Markov process. Strong limit theorems are developed for the ratio of the flow of particles from states i to j and the flow out of When the cumulative arrival of particles into the system up to time t, A (t) ∼ λtα, then a.s. When A (t)∼ λekt, then the flow between states must be normalized by the Laplace–Stieltjes transform of the conditional holding time distribution, in order to make the ratio an unbiased estimator of ρij.

Keywords

SEMI-MARKOV PROCESSESMULTIPARTICLE PROCESSESESTIMATION OF TRANSITION PROBABILITIESSTRONG LIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 696 - 706
Copyright
Copyright © Applied Probability Trust 1976 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Lewinski, D. A. (1967) A model for analyzing telephone costs. Presented at the Thirty-Second National Meeting of the Operations Research Society, Chicago.Google Scholar
Pyke, R. (1961) A Markov-renewal process with finitely many states. Ann. Math. Statist. 32, 1243–1259.CrossRefGoogle Scholar
Widder, D. (1941) The Laplace Transform. Princeton University Press.Google Scholar