Open Access
May 2016 Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum
Gábor Fukker, László Györfi, Péter Kevei
Bernoulli 22(2): 1026-1054 (May 2016). DOI: 10.3150/14-BEJ685


In this paper, we revisit the classical results on the generalized St. Petersburg sums. We determine the limit distribution of the St. Petersburg sum conditioning on its maximum, and we analyze how the limit depends on the value of the maximum. As an application, we obtain an infinite sum representation of the distribution function of the possible semistable limits. In the representation, each term corresponds to a given maximum, in particular this result explains that the semistable behavior is caused by the typical values of the maximum.


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Gábor Fukker. László Györfi. Péter Kevei. "Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum." Bernoulli 22 (2) 1026 - 1054, May 2016.


Received: 1 August 2013; Revised: 1 September 2014; Published: May 2016
First available in Project Euclid: 9 November 2015

zbMATH: 1336.60042
MathSciNet: MR3449807
Digital Object Identifier: 10.3150/14-BEJ685

Keywords: conditional limit theorem , generalized St. Petersburg distribution , merging theorem , semistable law

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 2 • May 2016
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