Horizons of fractional Brownian surfaces

Kenneth John Falconer; J Lévy Véhel

doi:10.1098/rspa.2000.0607

Horizons of fractional Brownian surfaces

Kenneth John Falconer, J Lévy Véhel

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the conjecture that the horizon of an index-alpha fractional Brownian surface has (almost surely) the same Holder exponents as the surface itself, with corresponding relationships for fractal dimensions. We establish this formally for the usual Brownian surface (where alpha = 1/2), and also for other alpha, 0 < alpha < 1, assuming a hypothesis concerning maxima of index-etc Brownian motion. We provide computational evidence that the conjecture is indeed true for all alpha.

Original language	English
Pages (from-to)	2153-2178
Number of pages	26
Journal	Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Volume	456
Issue number	2001
DOIs	https://doi.org/10.1098/rspa.2000.0607
Publication status	Published - 8 Sept 2000

Keywords

fractal
fractional Brownian motion
fractional Brownian field
horizon
dimension
MOTION

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AB - We investigate the conjecture that the horizon of an index-alpha fractional Brownian surface has (almost surely) the same Holder exponents as the surface itself, with corresponding relationships for fractal dimensions. We establish this formally for the usual Brownian surface (where alpha = 1/2), and also for other alpha, 0 < alpha < 1, assuming a hypothesis concerning maxima of index-etc Brownian motion. We provide computational evidence that the conjecture is indeed true for all alpha.

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KW - dimension

KW - MOTION

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Horizons of fractional Brownian surfaces

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Keywords

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