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The Generalized Multifractional Brownian Motion

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Abstract

It is well known that the fractional Brownian motion (FBM) is of great interest in modeling. However, its Hölder is the same all along its path and this restricts its field of application. Therefore, it would be useful to construct a Gaussian process extending the FBM and having a Hölder that is allowed to change. A partial answer to this problem is supplied by the multifractional Brownian motion (MBM); but the Hölder of the MBM must necessarily be continuous and this may be a drawback in some situations. In this paper we construct a Gaussian process generalizing the MBM and having a Hölder that can be a ‘very irregular’ function.

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Authors and Affiliations

  1. UFR MIG, LSP, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse

    Antoine Ayache

  2. Project Fractales, INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153, Le Chesnay, Cedex, France

    Jacques Levy Vehel

Authors
  1. Antoine Ayache
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  2. Jacques Levy Vehel
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Ayache, A., Vehel, J.L. The Generalized Multifractional Brownian Motion. Statistical Inference for Stochastic Processes 3, 7–18 (2000). https://doi.org/10.1023/A:1009901714819

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  • DOI: https://doi.org/10.1023/A:1009901714819

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