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- W1574242633 abstract "Let $S_n$ be the total gain in $n$ repeated St. Petersburg games. It is known that $n^{-1}(S_n-nlog_2n)$ converges in distribution to a random element $Y(t)$ along subsequences of the form $k(n)=2^{p(n)}t(n)$ with $p(n)=lceillog_2k(n)rceiltoinfty$ and $t(n)to tin[frac12,1]$. We determine the Hausdorff and box-counting dimension of the range and the graph for almost all sample paths of the stochastic process ${Y(t)}_{tin[1/2,1]}$. The results are compared to the fractal dimension of the corresponding limiting objects when gains are given by a deterministic sequence initiated by Hugo Steinhaus." @default.
- W1574242633 created "2016-06-24" @default.
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- W1574242633 date "2013-05-24" @default.
- W1574242633 modified "2023-09-27" @default.
- W1574242633 title "The dimension of the St. Petersburg game" @default.
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