Probability Theory
Large gains in the St. Petersburg game
[Grands gains dans le jeu de Saint Pétersbourg]
Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 563-566.

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.

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.03.026
Stoica, George 1

1 Department of Mathematical Sciences, University of New Brunswick, Saint John NB, E2L 4L5, Canada
@article{CRMATH_2008__346_9-10_563_0,
     author = {Stoica, George},
     title = {Large gains in the {St.} {Petersburg} game},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {563--566},
     publisher = {Elsevier},
     volume = {346},
     number = {9-10},
     year = {2008},
     doi = {10.1016/j.crma.2008.03.026},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.03.026/}
}
TY  - JOUR
AU  - Stoica, George
TI  - Large gains in the St. Petersburg game
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 563
EP  - 566
VL  - 346
IS  - 9-10
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.03.026/
DO  - 10.1016/j.crma.2008.03.026
LA  - en
ID  - CRMATH_2008__346_9-10_563_0
ER  - 
%0 Journal Article
%A Stoica, George
%T Large gains in the St. Petersburg game
%J Comptes Rendus. Mathématique
%D 2008
%P 563-566
%V 346
%N 9-10
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.03.026/
%R 10.1016/j.crma.2008.03.026
%G en
%F CRMATH_2008__346_9-10_563_0
Stoica, George. Large gains in the St. Petersburg game. Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 563-566. doi : 10.1016/j.crma.2008.03.026. http://www.numdam.org/articles/10.1016/j.crma.2008.03.026/

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

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

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

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

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

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

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

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

Cité par Sources :