Bernoulli

  • 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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Abstract

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1447077768

Digital Object Identifier
doi:10.3150/14-BEJ685

Mathematical Reviews number (MathSciNet)
MR3449807

Zentralblatt MATH identifier
1336.60042

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

Citation

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. https://projecteuclid.org/euclid.bj/1447077768


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