## The Annals of Probability

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

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

#### 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