Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum
Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum
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以其最大值为条件的广义圣彼得堡和的渐近行为
DOI：
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发表时间：
2013
期刊：
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通讯作者：
P. Kevei
中科院分区：
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作者：
Gábor Fukker;L. Gyorfi;P. Kevei
本文回顾了广义圣彼得堡和的经典结果。我们确定了圣彼得堡和条件在其最大值上的极限分布，并分析了极限是如何依赖于极大值的。作为应用，我们得到了可能的半稳定极限的分布函数的无穷和表示。在表示中，每一项对应于一个给定的最大值，特别是这一结果解释了半稳态行为是由最大值的典型值引起的。
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.