Extreme-trimmed St. Petersburg games
2015 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 96, 341-345 p.Article in journal (Refereed) Published
Let S-n, n >= 1, describe the successive sums of the payoffs in the classical St. Petersburg game. Feller's famous weak law, Feller (1945), states that s(n)/n log(2) n (sic) 1 as n -> infinity. However, almost sure convergence fails, more precisely, lim supn ->infinity S-n/n log(2) n = +infinity a.s. and lim inf(n ->infinity) S-n/n log(2) n = 1 a.s. as n -> infinity. Csorgo and Simons (1996) have shown that almost sure convergence holds for trimmed sums, that is, for S-n - max(1 <= k <= n) X-k and, moreover, that this remains true if the sums are trimmed by an arbitrary fixed number of maximal sums. A predecessor of the present paper was devoted to sums trimmed by the random number of maximal summands. The present paper concerns analogs for the random number of summands equal to the minimum, as well as analogs for joint trimmings. (C) 2014 Elsevier B.V. All rights reserved.
Place, publisher, year, edition, pages
2015. Vol. 96, 341-345 p.
St. Petersburg game, Trimmed sums, LLN, Convergence along subsequences
IdentifiersURN: urn:nbn:se:uu:diva-242860DOI: 10.1016/j.spl.2014.09.006ISI: 000346894500046OAI: oai:DiVA.org:uu-242860DiVA: diva2:787121