Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 1 (2013), 54-63.
Limit theorems for a generalized Feller game
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.
J. Appl. Probab., Volume 50, Number 1 (2013), 54-63.
First available in Project Euclid: 20 March 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G50: Sums of independent random variables; random walks
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