On the Asymptotic Behavior of the Harmonic Renewal Measure

M. S. Sgibnev

Journal of Theoretical Probability, 1998, vol. 11, issue 2, 371-382

Abstract: Abstract We study the tail behavior of the harmonic renewal measure U=Σ n=1 ∞ (1/n)F n* where F is a probability distribution with finite negative mean and F n * is the n-fold convolution of F. As an application of the obtained result on U, we give alternative proofs of some known results concerning the tail behavior of the supremum and the first positive sum of a random walk with negative drift.

Keywords: Harmonic renewal measure; tail behavior; subexponential and related distributions; supremum of a random walk; first positive sum; Banach algebras (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022627704800

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