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Records in the presence of a linear trend

Published online by Cambridge University Press:  01 July 2016

Rocco Ballerini  and
Sidney I. Resnick
Rocco Ballerini*
Affiliation:
University of Florida
Sidney I. Resnick*
Affiliation:
Colorado State University
*
∗Postal address: Department of Statistics, University of Florida, Gainesville, FL 32611, USA.
∗∗Present address: Department of Operations Research, Cornell University, Upson Hall, Ithaca, NY 14853, USA.
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Abstract

Records from the sequence Yn = Xn + cn, n ≧ 1 are analyzed, where {Xn} is a strictly stationary random sequence. We prove various limit theorems for the record rate, record times, and record values. The situation when {Xn} is a stationary Gaussian process is considered with special attention given to Gaussian ARMA sequences. Data for the 400 and 800 metre races are used to illustrate these results.

Keywords

STRONG MIXINGSUBADDITIVE PROCESSESGAUSSIAN SEQUENCES
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 801 - 828
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

This research was partially supported by NSF Grant DMS 8202335.

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