Comptes Rendus
Probability Theory
Large gains in the St. Petersburg game
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 563-566.

We consider the accumulated gains of geometric size in the St. Petersburg game and study the logarithmic tail asymptotics of their distribution.

Nous considérons des gains de taille géométrique accumulés dans le jeu de Saint Pétersbourg et étudions le comportement asymptotique de la queue de leur distribution.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.026

George Stoica 1

1 Department of Mathematical Sciences, University of New Brunswick, Saint John NB, E2L 4L5, Canada
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George Stoica. Large gains in the St. Petersburg game. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 563-566. doi : 10.1016/j.crma.2008.03.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.026/

[1] A. Adler Generalized one-sided laws of the iterated logarithm for random variables barely with or without finite mean, J. Theor. Prob., Volume 3 (1990), pp. 587-597

[2] Y.S. Chow; H. Robbins On sums of independent random variables with infinite moments and “fair games”, Proc. Nat. Acad. Sci. USA, Volume 47 (1961), pp. 330-335

[3] S. Csörgő; R. Dodunekova Limit Theorems for the Petersburg game (M.G. Hahn; D.M. Mason; D.C. Weiner, eds.), Sums, Trimmed Sums and Extremes, Progress in Probability, vol. 23, Birkhäuser Boston, 1991, pp. 285-315

[4] S. Csörgő; G. Simons A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games, Stat. Prob. Lett., Volume 26 (1996), pp. 65-73

[5] W. Feller Note on the law of large numbers and “fair” games, Ann. Math. Stat., Volume 16 (1945), pp. 301-304

[6] N. Gantert A note on logarithmic tail asymptotics and mixing, Stat. Prob. Lett., Volume 49 (2000), pp. 113-118

[7] A. Gut An extension of the Kolmogorov–Feller weak law of large numbers with an application to the St. Petersburg game, J. Theor. Prob., Volume 17 (2004), pp. 769-779

[8] Y. Hu; H. Nyrhinen Large deviations view points for heavy-tailed random walks, J. Theor. Prob., Volume 17 (2004), pp. 761-768

[9] A. Martin-Löf A limit theorem which clarifies the “Petersburg paradox”, J. Appl. Prob., Volume 22 (1985), pp. 634-643

[10] H. Steinhaus The so-called Petersburg paradox, Colloq. Math., Volume 2 (1949), pp. 56-58

[11] I. Vardi The St. Petersburg game and continued fractions, C. R. Acad. Sci. Paris, Ser. I, Volume 324 (1997), pp. 913-918

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