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Lacunary Fractional Brownian Motion

Published online by Cambridge University Press:  01 August 2012

Marianne Clausel
Marianne Clausel*
Affiliation:
Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050 du CNRS, Université Paris Est, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France. marianne.clausel@free.fr
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Abstract

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Keywords

Lacunary Gaussian fieldsnon uniqueness of the tangent fielduniform irregularitywavelets
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 16 , 2012 , pp. 352 - 374
Copyright
© EDP Sciences, SMAI, 2012

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