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Abstract

This paper is mainly concerned with the limit distribution of on the unit interval when the increasing sequence {n k} has bounded gaps, i.e., 1≤n k+1n k=O(1). By Bobkov–Götze [4], it was proved that the limiting variance must be less than 1/2 in this case. They proved that the centered Gaussian distribution with variance 1/4 together with mixtures of Gaussian distributions belonging to a huge class can be limit distributions. In this paper it is proved that any Gaussian distribution with variance less than 1/2 can be a limit distribution.

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Abstract  

We investigate the repeated and sequential portfolio St. Petersburg games. For the repeated St. Petersburg game, we show an upper bound on the tail distribution, which implies a strong law for a truncation. Moreover, we consider the problem of limit distribution. For the sequential portfolio St. Petersburg game, we obtain tight asymptotic results for the growth rate of the game.

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2001 Takács, L. , Limit distributions for queues and random rooted trees, J. Appl. Math. Stochastic Anal. , 6:3 (1993), 189

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