Limit Theorems for a Generalized ST Petersburg Game
Limit Theorems for a Generalized ST Petersburg Game
复制标题
广义 ST Petersburg 博弈的极限定理
DOI：
10.1239/jap/1285335407
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发表时间：
2010
影响因子：
1
通讯作者：
A. Gut
中科院分区：
文献类型：
--
作者：
A. Gut
本文的主题是一个广义圣彼得堡对策，其中收益X的分布由P(X = sr (k-1)/α) = pq k-1, k = 1,2，…给出，其中P + q = 1, s = 1 / P, r = 1 / q，且0 < α≤1。对于α = 1的情况，我们扩展了Feller的经典弱定律和Martin-Löf的分布收敛定理沿2n -子序列。0 < α < 1的类比在分布上收敛于一个指标为α的不对称稳定律。最后，给出了多项式和几何大小总增益以及极值的一些极限定理。
The topic of the present paper is a generalized St Petersburg game in which the distribution of the payoff X is given by P(X = sr (k-1)/α) = pq k-1, k = 1, 2,…, where p + q = 1, s = 1 / p, r = 1 / q, and 0 < α ≤ 1. For the case in which α = 1, we extend Feller's classical weak law and Martin-Löf's theorem on convergence in distribution along the 2 n -subsequence. The analog for 0 < α < 1 turns out to converge in distribution to an asymmetric stable law with index α. Finally, some limit theorems for polynomial and geometric size total gains, as well as for extremes, are given.