Submultiplicative moments of the supremum of a random walk with negative drift

M. S. Sgibnev

Statistics & Probability Letters, 1997, vol. 32, issue 4, 377-383

Abstract: Let {Sn} be the sequence of partial sums of independent identically distributed random variables with negative mean. Necessary and sufficient conditions are obtained for E[phi](M[infinity]) to be finite, where [phi](x) is a non-decreasing submultiplicative function, i.e. [phi](x + y)[less-than-or-equals, slant][phi](x)[phi](y), and M[infinity] = sup{0, S1, S2,...}. This generalizes a well-known result on moments of M[infinity] proved by Kiefer and Wolfowitz (1956). Submultiplicative moments of the first positive sum are also considered.

Keywords: Random; walk; Supremum; First; positive; sum; Moments; Submultiplicative; functions; Wiener-Hopf; factorization; Infinite; divisibility; Banach; algebras (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (5)

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