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Nonstandard analysis, fractal properties and Brownian motion

Show simple item record Potgieter, Paul 2015-07-07T06:26:00Z 2015-07-07T06:26:00Z 2009-03
dc.identifier.citation Potgieter, p. (2009). Nonstandard analysis, fractal properties and Brownian motion. Fractals 17(01), 117-129. en
dc.identifier.issn 0218-348X
dc.description.abstract Using Loeb measure theory, it is possible to construct Lebesgue or even Wiener measure as a hyperfinite counting measure. In this paper I explore an extension of the idea to Hausdorff measure, which yields a hyperfinite formulation of Hausdorff dimension. In cases where the problem of dimension can be interpreted as an equivalent problem on a hyperfinite time line, this can lead to a simple and intuitively satisfying proof. For instance, I shall later consider certain properties of Brownian motion, and present nonstandard proofs which are somewhat easier than the original, and also seem to obey certain statistical “rules of thumb”. I now provide a short overview of the necessary nonstandard analysis as well as the standard formulation of Hausdorff dimension, since the nonstandard version will follow the same style and notation. en
dc.language.iso en en
dc.subject Frostman’s lemma, Nonstandard Hausdorff dimension, Brownian motion en
dc.title Nonstandard analysis, fractal properties and Brownian motion en
dc.type Article en
dc.description.department Decision Sciences en

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