Abstract
We determine all possible subsequences \(\left\{ {n_k } \right\}_{k = 1}^\infty\)of the positive integers for which the suitably centered and normalized total gain S nk in n k Petersburg games has an asymptotic distribution as k → ∞, and identify the corresponding set of Hmiting distributions. We also solve all the companion problems for lightly, moderately, and heavily trimmed versions of the sum S nk and for the respective sums of extreme values in S nk .
Partially Supported by the Hungarian National Foundation for Scientific Research, Grants 1808/86 and 457/88.
Partially Supported by the Ministry of Culture, Science and Educational of Bulgaria, Contract No. 16848-F3.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. CSÖRGŐ, An extreme-sum approximation to infinitely divisible laws without a normal component. In: Probability on Vector Spaces IV. (S. Cambanis and A. Weron, eds.) pp. 47–58. Lecture Notes in Mathematics 1391, Springer, Berlin, 1989.
S. CSÖRGÖ, A probabilistic approach to domains of partial attraction. Adv. in Appl Math. 11 (1990), to appear.
S. CSÖRGÖ, E. HAEUSLER, and D. M. MASON, A probabilistic approach to the asymptotic distribution of sums of independent, identically distributed random variables. Adv. in Appl. Math. 9(1988), 259–333.
S. CSÖRGÖ, E. HAEUSLER, and D. M. MASON, The asymptotic distribution of trimmed sums. Ann. Probab. 16(1988), 672–699.
S. CSÖRGÖ, E. HAEUSLER, and D. M. MASON, The asymptotic distribution of extreme sums. Ann. Probab. 19 (1991), to appear.
S. CSÖRGÖ, E. HAEUSLER, and D. M. MASON, The quantile - transform - empirical - process approach to limit theorems for sums of order statistics. In: Sums, Trimmed Sums, and Extremes (M. G. Hahn, D. M. Mason, and D. C. Weiner, eds.). Birkhäuser, Basel, 1990.
S. CSÖRGÖ and D. M. MASON, Intermediate sums and stochastic compactness of maxima. Submitted.
W. FELLER, An Introduction to Probability Theory and its Applications, Vol. l. Wiley, New York, 1950.
P. LEVY, Theorie de Vaddition des variables aleatoires, ed. Gauthier - Villars, Paris, 1954.
A. MARTIN - LÖF, A limit theorem which clarifies the ‘Petersburg paradox’. J. Appl Probab. 22(1985), 634–643.
G. SHAFER, The St. Petersburg paradox. In:Encyclopedia of Statistical Sciences, Vol 8 (S. Kotz, N. L. Johnson, and C. B. Read, eds.), pp. 865–870. Wiley, New-York, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Birkhäuser Boston
About this chapter
Cite this chapter
Csörgő, S., Dodunekova, R. (1991). Limit Theorems for the Petersburg Game. In: Hahn, M.G., Mason, D.M., Weiner, D.C. (eds) Sums, Trimmed Sums and Extremes. Progress in Probability, vol 23. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6793-2_9
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6793-2_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-6795-6
Online ISBN: 978-1-4684-6793-2
eBook Packages: Springer Book Archive