Central limit theorems for the number of records in discrete models

DOI10.1239/aap/1127483747zbMath1080.60016OpenAlexW1990101125MaRDI QIDQ5697202

F. Javier López, Raúl Gouet, Gerardo Sanz

Publication date: 17 October 2005

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1127483747

zbMATH Keywords

asymptotic normalitymartingalemaximumcounting processdiscrete distribution

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70)

Related Items

A characteristic martingale related to the counting process of records, Limit laws for the cumulative number of ties for the maximum in a random sequence, A limit theorem for the survival probability of a simple random walk among power-law renewal obstacles, Asymptotic normality for the counting process of weak records and \(\delta \)-records in discrete models, Asymptotic normality for the number of records from general distributions, Modeling record-breaking stock prices, Laws of large numbers for the number of weak records

Cites Work

• Mellin transforms and asymptotics: Finite differences and Rice's integrals
• Combinatorics of geometrically distributed random variables: Left-to-right maxima
• Limit theorems for records from discrete distributions
• A martingale approach to strong convergence of the number of records
• Normal approximations of the number of records in geometrically distributed random variables
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