Journal of Applied Probability

Limit theorems for a generalized Feller game

Keisuke Matsumoto and Toshio Nakata

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In this paper we study limit theorems for the Feller game which is constructed from one-dimensional simple symmetric random walks, and corresponds to the St. Petersburg game. Motivated by a generalization of the St. Petersburg game which was investigated by Gut (2010), we generalize the Feller game by introducing the parameter α. We investigate limit distributions of the generalized Feller game corresponding to the results of Gut. Firstly, we give the weak law of large numbers for α=1. Moreover, for 0<α≤1, we have convergence in distribution to a stable law with index α. Finally, some limit theorems for a polynomial size and a geometric size deviation are given.

Article information

J. Appl. Probab., Volume 50, Number 1 (2013), 54-63.

First available in Project Euclid: 20 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G50: Sums of independent random variables; random walks

Feller's game simple symmetric random walk law of large numbers stable law extremes


Matsumoto, Keisuke; Nakata, Toshio. Limit theorems for a generalized Feller game. J. Appl. Probab. 50 (2013), no. 1, 54--63. doi:10.1239/jap/1363784424.

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