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Generalized Multifractional Brownian Motion: Definition and Preliminary Results

Abstract : The Multifractional Brownian Motion (MBM) is a generalization of the well known Fractional Brownian Motion. One of the main reasons that makes the MBM interesting for modelization, is that one can prescribe its regularity: given any Hölder function H(t), with values in ]0,1[, one can construct an MBM admitting at any t0, a Hölder exponent equal to H(t0). However, the continuity of the function H(t) is sometimes undesirable, since it restricts the field of application. In this work we define a gaussian process, called the Generalized Multifractional Brownian Motion (GMBM) that extends the MBM. This process will also depend on a functional parameter H(t) that belongs to a set , but will be much more larger than the space of Hölder functions.
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https://hal.inria.fr/inria-00578657
Contributor : Lisandro Fermin <>
Submitted on : Monday, March 21, 2011 - 6:19:32 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
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Antoine Ayache, Jacques Lévy Véhel. Generalized Multifractional Brownian Motion: Definition and Preliminary Results. M. Dekking, J. Lévy Véhel, E. Lutton and C. Tricot. Fractals - Theory and Applications in Engineering, Springer, 1999. ⟨inria-00578657⟩

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