The Length of the Longest Head-Run in a Model with Long Range Dependence

Thomas M. Lewis ()
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Thomas M. Lewis: Furman University

Journal of Theoretical Probability, 2001, vol. 14, issue 2, 357-378

Abstract: Abstract In this paper, we construct stationary sequences of random variables {χ i : i≥0} taking values ±1 with probability 1/2 and we prove an Erdös–Rényi law of large numbers for the length of the longest run of consecutive +1's in the sample {χ0,..., χ n }. Our model, which is called random walk in random scenery, exhibits long-range, positive dependence.

Keywords: random walk in random scenery; head-runs; Erdös–Rényi law of large numbers (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1011107629319

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