A uniform dimension result for two-dimensional fractional multiplicative processes

Xiong Jin

doi:10.1214/12-AIHP509

A uniform dimension result for two-dimensional fractional multiplicative processes

Xiong Jin

Pure Mathematics

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Abstract

We show that a two-dimensional fractional multiplicative process has a uniform Hausdorff dimension result if and only if the two parameters of the process coincide.

Original language	English
Pages (from-to)	512--523
Journal	Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Volume	50
Issue number	2
DOIs	https://doi.org/10.1214/12-AIHP509
Publication status	Published - Mar 2014

Keywords

self-similar processes
Hausdorff dimension
Fractional multiplicative processes
Uniform dimension result
Level sets

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10.1214/12-AIHP509

Jin2014_AnnInstHPoincareProbStat50-2_Uniform
Copyright (c) Association des Publications de l’Institut Henri Poincaré, 2014. This work is made available online in accordance with the publisher’s policies. This is the final published version of the work which was originally published at https://doi.org/10.1214/12-AIHP509
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Cite this

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title = "A uniform dimension result for two-dimensional fractional multiplicative processes",

abstract = "We show that a two-dimensional fractional multiplicative process has a uniform Hausdorff dimension result if and only if the two parameters of the process coincide.",

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KW - self-similar processes

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KW - Fractional multiplicative processes

KW - Uniform dimension result

KW - Level sets

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M3 - Article

SN - 0246-0203

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JF - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

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A uniform dimension result for two-dimensional fractional multiplicative processes

Abstract

Keywords

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