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Records in the presence of a linear trend

  • Rocco Ballerini (a1) and Sidney I. Resnick (a2)
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.

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Corresponding author
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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This research was partially supported by NSF Grant DMS 8202335.

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References
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Advances in Applied Probability
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