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Extremal processes and record value times

Published online by Cambridge University Press:  14 July 2016

Sidney I. Resnick
Sidney I. Resnick*
Affiliation:
Stanford University
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Abstract

Let {Xn , n ≧ 1} be i.i.d. and Yn = max {X 1,…, Xn }. Xj is a record value of {Xn } if Yj > Yj– 1 The record value times are Ln, n ≧ 1 and inter-record times are Δn , n ≧ 1. The known limiting behavior of {Ln } and {Δn } is close to that of a non-homogeneous Poisson process and an explanation of this is obtained by embedding {Yn } in a suitable extremal process which jumps according to a non-homogeneous Poisson process.

Keywords

RECORD VALUERECORD TIMESPOISSON PROCESSEXTREMAL PROCESSMAXIMA

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973, pp. 864 - 868
Copyright
Copyright © Applied Probability Trust 1973 

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