• Bernoulli
  • Volume 22, Number 2 (2016), 1026-1054.

Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum

Gábor Fukker, László Györfi, and Péter Kevei

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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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Bernoulli, Volume 22, Number 2 (2016), 1026-1054.

Received: August 2013
Revised: September 2014
First available in Project Euclid: 9 November 2015

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conditional limit theorem generalized St. Petersburg distribution merging theorem semistable law


Fukker, Gábor; Györfi, László; Kevei, Péter. Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum. Bernoulli 22 (2016), no. 2, 1026--1054. doi:10.3150/14-BEJ685.

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