The accuracy of merging approximation in generalized St. Petersburg games

Details The accuracy of merging approximation in generalized St. Petersburg games The accuracy of merging approximation in generalized St. Petersburg games

2007-10-07

arxiv.org/abs/0710.1438v2

Mathematics

Probability

30 pages long version (to appear in Journal of Theoretical Probability); some corrected typos

Scientific paper

10.1007/s10959-009-0247-1

Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games, extending the short expansions due to Cs\"org\H{o}, S., Merging asymptotic expansions in generalized St. Petersburg games, \textit{Acta Sci. Math. (Szeged)} \textbf{73} 297--331, 2007. These expansions are given in terms of suitably chosen members from the classes of subsequential semistable infinitely divisible asymptotic distribution functions and certain derivatives of these functions. The length of the expansion depends upon the tail parameter. Both uniform and nonuniform bounds are presented.

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