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Records in the presence of a linear trend

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

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.

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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Advances in Applied Probability
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