The Annals of Probability

On the Tail Behaviour of Record-Time Distributions in a Random Record Process

Mark Westcott

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Abstract

Consider a sequence of independent and identically distributed random variables attached to the points of an independent point process $P$. The random record process is the epochs of successive maxima in this sequence. In this paper necessary and sufficient conditions are found to ensure a certain tail behaviour for the distributions of times to successive records, and interrecord times, when $P$ is a renewal process with relatively stable partial sums for its intervals.

Article information

Source
Ann. Probab., Volume 7, Number 5 (1979), 868-873.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994946

Digital Object Identifier
doi:10.1214/aop/1176994946

Mathematical Reviews number (MathSciNet)
MR542137

Zentralblatt MATH identifier
0416.60061

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 60G50: Sums of independent random variables; random walks 60K05: Renewal theory 60K99: None of the above, but in this section

Keywords
Point process random record process relatively stable renewal process tails of distributions

Citation

Westcott, Mark. On the Tail Behaviour of Record-Time Distributions in a Random Record Process. Ann. Probab. 7 (1979), no. 5, 868--873. doi:10.1214/aop/1176994946. https://projecteuclid.org/euclid.aop/1176994946


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