On the Hausdorff Dimension of the Set Generated by Exceptional Oscillations of a Two-Parameter Wiener Process

Zacharie Dindar

Journal of Multivariate Analysis, 2001, vol. 79, issue 1, 52-70

Abstract: S. Orey and S. J. Taylor (1974, Proc. London Math. Soc.28, 174-192) proved that for 0[less-than-or-equals, slant][lambda][less-than-or-equals, slant]1 the set E([lambda])={t[set membership, variant][0, 1] : lim suph[downwards arrow]0(2h log(1/h))-1/2 (W'(t+h)-W'(t))[greater-or-equal, slanted][lambda]} has Hausdorff dimension dim E([lambda])=1-[lambda]2 a.s. where W'(t) is a standard Wiener process. A corresponding result is obtained when W' is replaced by a two-parameter Wiener process.

Keywords: random; fractals; Wiener; process (search for similar items in EconPapers)
Date: 2001
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