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Random fractals generated by a local Gaussian process indexed by a class of functions

Published online by Cambridge University Press:  05 January 2012

Claire Coiffard
Claire Coiffard*
Affiliation:
LSTA, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France; claire.coiffard@centrale-marseille.fr
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Abstract

In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc. 28 (1974) 174–192]relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.

Keywords

Random fractalsHausdorff dimensionWiener process
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 249 - 269
Copyright
© EDP Sciences, SMAI, 2011

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