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Exact expressions for the moments of ladder heights

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Abstract

With the aid of the formula for the Laplace transform of a contraction of a distribution on the positive semiaxis the formulas for moments of the ascending ladder height are deduced for each of the three cases: the null, positive and negative expectation of a step in the random walk. The results are formulated in terms of the moments and integral functionals of the characteristic function of the step function. Despite the complexity of the proof the final formulas are comparatively simple.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    S. V. Nagaev

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  1. S. V. Nagaev
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Correspondence to S. V. Nagaev.

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Original Russian Text Copyright © 2010 Nagaev S. V.

The author was supported by the Russian Foundation for Basic Research (Grant 09-01-0048-a).

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 4, pp. 848–870, July–August, 2010.

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Nagaev, S. Exact expressions for the moments of ladder heights. Sib Math J 51, 675–695 (2010). https://doi.org/10.1007/s11202-010-0069-5

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  • DOI: https://doi.org/10.1007/s11202-010-0069-5

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