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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 sumconditioning on its maximum, and we analyze how the limit depends on the valueof the maximum. As an application, we obtain an infinite sum representation ofthe distribution function of the possible semistable limits. In therepresentation, each term corresponds to a given maximum, in particular thisresult explains that the semistable behavior is caused by the typical values ofthe maximum.

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