A note on the maximum of a random walk

W. Stadje

Statistics & Probability Letters, 1995, vol. 23, issue 3, 227-231

Abstract: For an integer-valued, aperiodic random walk (Sn)n [greater-or-equal, slanted] 1 with negative drift we consider its maximum M and M+, its maximum before first attaining a nonpositive value. As a converse to well-known results on the asymptotic behavior of mn = P(M [greater-or-equal, slanted] n) and rn = P(M+ [greater-or-equal, slanted] n), it is shown that any of the relations mn ~ cr-n or rn ~ cr-n (c > 1, r > 1) implies that E(rS1) = 1.

Keywords: Integer-valued; random; walk; Maximum; Moment-generating; function (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (1)

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