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On discrete time extremal processes

Published online by Cambridge University Press:  01 July 2016

R. W. Shorrock
R. W. Shorrock*
Affiliation:
Université de Montréal
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Abstract

Upper record values and times and inter-record times are studied in their rôles as embedded structures in discrete time extremal processes. Various continuous time approximations to the discrete-time processes are analysed, especially as processes over their state spaces. Discrete time processes, suitably normalized after crossing a threshold T, are shown to converge to limiting continuous time processes as T → ∞ under suitable assumptions on the underlying CDF F, for example, when 1 — F varies regularly at ∞, and more generally. Discrete time extremal processes viewed as processes over their state spaces are noted to have an interesting interpretation in terms of processes of population growth.

Keywords

RECORDSPOPULATION GROWTHINDEPENDENT INCREMENT POINT PROCESSLIMIT LAWS
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 3 , September 1974 , pp. 580 - 592
Copyright
Copyright © Applied Probability Trust 1974 

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References

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