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Limit theorems for a generalized St Petersburg game
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2010 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 3, 752-760 p.Article in journal (Refereed) Published
Abstract [en]

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)/alpha)) = pq(k-1), k = 1,2, ..., where p + q = 1, s = l/p, r = 1/q, and 0 < alpha <= 1. For the case in which alpha = 1, we extend Feller's classical weak law and Martin-Lof's theorem on convergence in distribution along the 2"-subsequence. The analog for 0 < alpha < 1 turns out to converge in distribution to an asymmetric stable law with index a. Finally, some limit theorems for polynomial and geometric size total gains, as well as for extremes, are given.

Place, publisher, year, edition, pages
2010. Vol. 47, no 3, 752-760 p.
Keyword [en]
St Petersburg game, sums of i.i.d. random variables, Feller's weak law of large numbers, domains of attraction, convergence along subsequences, extremes, stable law, slow variation, regular variation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-134148DOI: 10.1239/jap/1285335407ISI: 000282856000009OAI: oai:DiVA.org:uu-134148DiVA: diva2:373449
Available from: 2010-11-30 Created: 2010-11-22 Last updated: 2010-11-30Bibliographically approved

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