Correlations Between Record Events in Sequences of Random Variables with a Linear Trend

The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics beyond the case of i.i.d. random variables have received much...

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Bibliographic Details
Published inJournal of statistical physics Vol. 144; no. 6; pp. 1206 - 1222
Main Authors Wergen, Gregor, Franke, Jasper, Krug, Joachim
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.09.2011
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Records
Correlations
Extreme value statistics
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Summary:The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics beyond the case of i.i.d. random variables have received much attention, but the question of independence of record events has not been addressed systematically. In this paper, we study this question in detail for the case of independent, non-identically distributed random variables, specifically, for random variables with a linearly moving mean. We find a rich pattern of positive and negative correlations, and show how their asymptotics is determined by the universality classes of extreme value statistics.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-011-0307-7