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Applications of the key renewal theorem: crudely regenerative processes

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Richard F. Serfozo
Richard F. Serfozo*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332–0205, USA.
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Abstract

Limit Statements obtainable by the key renewal theorem are of the form EXt = v(t) + o(1), as t →∞. We show how to delineate the limit function v for processes X associated with crudely regenerative phenomena. Included are refinements of classical limit theorems for Markov and regenerative processes, limits of sums of stationary random variables, and limits for integrals and derivatives of EXt.

Keywords

RENEWAL PROCESSMARKOV PROCESSSEMI-STATIONARY PROCESSLIMIT THEOREMRATE OF CONVERGENCE

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60G99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 384 - 395
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

This research was supported in part by the Air Force Office of Scientific Research under contract 89–0407 and NSF grant DDM-900–7532.

References

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