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 Sibirsk. Mat. Zh., 2010, Volume 51, Number 4, Pages 848–870 (Mi smj2130)

Exact expressions for the moments of ladder heights

S. V. Nagaev

Sobolev Institute of Mathematics, Novosibirsk, Russia

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.

Keywords: ladder height, moment, Laplace transform, Spitzer series, Winer–Hopf identity, Bruno formula.

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English version:
Siberian Mathematical Journal, 2010, 51:4, 675–695

Bibliographic databases:

UDC: 519.2

Citation: S. V. Nagaev, “Exact expressions for the moments of ladder heights”, Sibirsk. Mat. Zh., 51:4 (2010), 848–870; Siberian Math. J., 51:4 (2010), 675–695

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Goldberg D.A., Katz-Rogozhnikov D.A., Lu Y., Sharma M., Squillante M.S., “Asymptotic Optimality of Constant-Order Policies For Lost Sales Inventory Models With Large Lead Times”, Math. Oper. Res., 41:3 (2016), 898–913
2. Gokpinar F., Khaniyev T.A., Aliyev R., “Approximation Formulas For the Moments of the Boundary Functional of a Gaussian Random Walk With Positive Drift By Using Siegmund'S Formula”, Commun. Stat.-Simul. Comput., 48:9 (2019), 2679–2688
3. Khaniyev T., Sevinc O.A., “Limit Theorem For a Semi-Markovian Random Walk With General Interference of Chance”, Sains Malays., 49:4 (2020), 919–928
4. S. V. Nagaev, “Otsenka summy ryada Spitsera i ee obobschenie”, Teoriya veroyatn. i ee primen., 66:1 (2021), 110–128
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