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Records in the Presence of a Linear Trend

Rocco Ballerini and Sidney I. Resnick
Advances in Applied Probability
Vol. 19, No. 4 (Dec., 1987), pp. 801-828
DOI: 10.2307/1427103
Stable URL: http://www.jstor.org/stable/1427103
Page Count: 28
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Records in the Presence of a Linear Trend
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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.

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