Bernoulli

  • Bernoulli
  • Volume 13, Number 3 (2007), 754-781.

Asymptotic normality for the counting process of weak records and δ-records in discrete models

Raúl Gouet, F. Javier López, and Gerardo Sanz

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Abstract

Let {Xn, n≥1} be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call Xn a δ-record if Xn>max {X1, …, Xn−1}+δ, where δ is an integer constant. We use martingale arguments to show that the counting process of δ-records among the first n observations, suitably centered and scaled, is asymptotically normally distributed for δ≠0. In particular, taking δ=−1 we obtain a central limit theorem for the number of weak records.

Article information

Source
Bernoulli, Volume 13, Number 3 (2007), 754-781.

Dates
First available in Project Euclid: 7 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1186503485

Digital Object Identifier
doi:10.3150/07-BEJ6027

Mathematical Reviews number (MathSciNet)
MR2348749

Zentralblatt MATH identifier
1138.60309

Keywords
Central limit theorem martingale record weak record

Citation

Gouet, Raúl; López, F. Javier; Sanz, Gerardo. Asymptotic normality for the counting process of weak records and δ -records in discrete models. Bernoulli 13 (2007), no. 3, 754--781. doi:10.3150/07-BEJ6027. https://projecteuclid.org/euclid.bj/1186503485


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