Limit theorems for a generalized St Petersburg game

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

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

MATHEMATICS

MATEMATIK

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