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On the Asymptotic Behavior of the Harmonic Renewal Measure

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  • M. S. Sgibnev

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.

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  • M. S. Sgibnev, 1998. "On the Asymptotic Behavior of the Harmonic Renewal Measure," Journal of Theoretical Probability, Springer, vol. 11(2), pages 371-382, April.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:2:d:10.1023_a:1022627704800
    DOI: 10.1023/A:1022627704800
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    References listed on IDEAS

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    1. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    2. Veraverbeke, N., 1977. "Asymptotic behaviour of Wiener-Hopf factors of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 27-37, February.
    3. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    4. Alsmeyer, Gerold, 1991. "Some relations between harmonic renewal measures and certain first passage times," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 19-27, July.
    5. Stam, A. J., 1991. "Some theorems on harmonic renewal measures," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 277-285, December.
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