Dimension results related to the St. Petersburg game

Kern, P.; Wedrich, L.

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Tytuł artykułu

Dimension results related to the St. Petersburg game

Autorzy

Kern P. , Wedrich L.

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Warianty tytułu

Języki publikacji

Abstrakty

Let S_n be the total gain in n repeated St. Petersburg games. It is known that n⁻¹(S_n − n log₂ n) converges in distribution along certain geometrically increasing subsequences and its possible limiting random variables can be parametrized as Y (t) with t ∈ [1/2, 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)}_{t∈[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.

Słowa kluczowe

St. Petersburg game semistable process sample path semi-selfsimilarity range graph Hausdorff dimension box-counting dimension Steinhaus sequence iterated function system self-affine set

Wydawca

Wrocław University of Science and Technology

Czasopismo

Probability and Mathematical Statistics

Rocznik

2014

Tom

Vol. 34, Fasc. 1

Strony

97--117

Opis fizyczny

Bibliogr. 41 poz., wykr.

Twórcy

autor

Kern P.

kern@math.uni-duesseldorf.de

Institute of Mathematics, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

autor

Wedrich L.

wedrich@math.uni-duesseldorf.de

Institute of Mathematics, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

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Bibliografia

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