Large gains in the St. Petersburg game

Stoica, George

doi:10.1016/j.crma.2008.03.026

Cited by 14 publications

(9 citation statements)

References 12 publications

(16 reference statements)

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“…Next, for sufficiently large x ∈ R + , using (16), we see that Next, for sufficiently large x ∈ R + , using (16), we see that…”

Section: Lemma 2 For X (α) Defined Bymentioning

confidence: 90%

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Limit Theorems for a Generalized Feller Game

Matsumoto¹,

Nakata²

2013

J. Appl. Probab.

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In this paper we study limit theorems for the Feller game which is constructed from onedimensional 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.

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“…Next, for sufficiently large x ∈ R + , using (16), we see that Next, for sufficiently large x ∈ R + , using (16), we see that…”

Section: Lemma 2 For X (α) Defined Bymentioning

confidence: 90%

“…Finally, referring to results in[10] and[16], we give results for a polynomial size and a geometric size deviation of S Section 5. Comparing Theorem 2 and Theorem 3(ii) for α = 1, we confirm that the Feller game and the St. Petersburg game have different properties.…”

mentioning

confidence: 99%

Limit Theorems for a Generalized Feller Game

Matsumoto¹,

Nakata²

2013

J. Appl. Probab.

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“…Turning to geometric size deviations, Stoica [14] provided a result for the classical St Petersburg game to the effect that, for any ε > 0 and b > 1,…”

Section: Polynomial and Geometric Size Deviationsmentioning

confidence: 99%

“…The upper bound follows by copying the lower half of page 565 of [14], replacing b n by b n/α at appropriate places. We omit the details.…”

Section: Polynomial and Geometric Size Deviationsmentioning

confidence: 99%

Limit Theorems for a Generalized ST Petersburg Game

Gut

2010

Journal of Applied Probability

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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.

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“…[8, p. 452]) for 0 < α ≤ 1. Finally, referring to results in[10] and[16], we give results for a polynomial size and a geometric size deviation of S…”

mentioning

confidence: 99%

Limit Theorems for a Generalized Feller Game

Matsumoto

Nakata

2013

Journal of Applied Probability

View full text Add to dashboard Cite

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.

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Large gains in the St. Petersburg game

Cited by 14 publications

References 12 publications

Limit Theorems for a Generalized Feller Game

Limit Theorems for a Generalized Feller Game

Limit Theorems for a Generalized ST Petersburg Game

Limit Theorems for a Generalized Feller Game

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