Journal of Applied Probability

Limit theorems for a generalized Feller game

Keisuke Matsumoto and Toshio Nakata

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Abstract

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

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

Dates
First available in Project Euclid: 20 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1363784424

Digital Object Identifier
doi:10.1239/jap/1363784424

Mathematical Reviews number (MathSciNet)
MR3076772

Zentralblatt MATH identifier
1274.60070

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

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

Citation

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. https://projecteuclid.org/euclid.jap/1363784424


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