Albert Benassi
Blaise Pascal University
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Featured researches published by Albert Benassi.
Revista Matematica Iberoamericana | 1997
Albert Benassi; Daniel Roux; Stéphane Jaffard
We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol of the pseudodifferential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.
Statistics & Probability Letters | 1998
Albert Benassi; Serge Cohen; Jacques Istas
Gaussian processes that are multifractional are studied in this paper. By multifractional processes we mean that they behave locally like a fractional Brownian motion, but the fractional index is no more a constant: it is a function. We introduce estimators of this multifractional function based on discrete observations of one sample path of the process and we study their asymptotical behavior as the mesh decreases to zero.
Stochastic Processes and their Applications | 1998
Albert Benassi; Serge Cohen; Jacques Istas; Stéphane Jaffard
In this paper, a class of Gaussian processes, having locally the same fractal properties as fractional Brownian motion, is studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. A time dependency of the integrand of the classical Wiener integral, associated with the fractional Brownian motion, is introduced. We show how to identify the asymptotic expansion for high frequencies of these integrands on one sample path. Then, the identification of the first terms of this expansion is used to solve some filtering problems. Furthermore, rates of convergence of the estimators are then given.
Statistical Inference for Stochastic Processes | 2000
Albert Benassi; P. Bertrand; Serge Cohen; Jacques Istas
We propose a semi-parametric estimator for a piece-wise constant Hurst coefficient of a step fractional Brownian motion (SFBM). For the applications, we want to detect abrupt changes of the Hurst index (which represents long-range correlation) for a Gaussian process with a.s. continuous paths. The previous model of multifractional Brownian motion give a.s. discontinuous paths at change times of the Hurst index. Thus, we first propose a new kind of Fractional Brownian Motion, the SFBM and prove some (Hölder) continuity results. After, we propose an estimator of the piecewise constant Hurst parameter and prove its consistency.
Lecture Notes in Mathematics | 2005
Antoine Ayache; Albert Benassi; Serge Cohen; Jacques Lévy Véhel
In this article a class of multifractional processes is introduced, called Generalized Multifractional Gaussian Process (GMGP). For such multifractional models, the Hurst exponent of the celebrated Fractional Brownian Motion is replaced by a function, called the multifractional function, which may be irregular. The main aim of this paper is to show how to identify irregular multifractional functions in the setting of GMGP. Examples of discontinuous multifractional functions are also given.
Comptes Rendus Mathematique | 2003
Albert Benassi; Serge Cohen; Jacques Istas
Abstract Let X be a locally self-similar stochastic process of index 0 H C H − e for all e >0. Then the Hausdorff dimension of the graph of X is a.s. 2− H . To cite this article: A. Benassi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).
british machine vision conference | 2000
Sébastien Deguy; Christophe Debain; Albert Benassi
We present a new method of fractal-based texture analysis, using the multiscale fractional Brownian motiontexture model, and a new parameter, intermittency. The intermittency parameter describes a degree of presence of the textural information: a low value of implies a very lacunar texture. The multi-scale fractional Brownian motion model allows to construct multiregime textures in the frequency domain. Adding intermittency to this model, we compose the intermittent multi-scale fractional Brownian motion model: the Hurst and intermittency parameters of such processes are functions and depending on a scale . The texture is thereby seen as the fusion of structures and details. The structure of the texture is analyzed with the large values of , corresponding to the low frequency content of the texture. The details of the texture are analyzed with the small values of , related to the high frequency content of the texture. The texture is then characterized by all the estimated values of and , for all the scales of analysis. The method allows a multi-frequency analysis, permitting the choice of significant scales in a classification task. An application to the classification of corn silage texture images, for which the low frequency content is determining, is proposed.
Comptes Rendus De L Academie Des Sciences Serie I-mathematique | 1999
Albert Benassi; P. Bertrand; Serge Cohen; Jacques Istas
Resume Nous proposons un modele de processus stochastique gaussien multifractionnaire a trajectoires continues, mais dont la fonction d’echelle presente des discontinuites, i.e. une fonction d’echelle constante par morceaux (SFBM: « Step Fractional Brownian Motion »). Ceci permet de modeliser des phenomenes, a trajectoires continues, comportant des changements abrupts de nature a certains moments. Nous construisons le modele theorique, puis nous proposons un estimateur de la fonction d’echelle du processus en detectant les instants de rupture et en estimant les valeurs de la fonction d’echelle entre les instants de rupture.
Revista Matematica Iberoamericana | 2003
Albert Benassi; Daniel Roux
Let M be a random measure and L be an elliptic pseudo-differential operator on Rd. We study the solution of the stochastic problem LX = M, X(O) = O when some homogeneity and integrability conditions are assumed. If M is a Gaussian measure the process X belongs to the class of Elliptic Gaussian Processes which has already been studied. Here the law of M is not necessarily Gaussian. We characterize the solutions X which are self-similar and with stationary increments in terms of the driving mcasure M. Then we use appropriate wavelet bases to expand these solutions and we give regularity results. In the last section it is shown how a percolation forest can help with constructing a self-similar Elliptic Process with non stable law.
Journal of the Atmospheric Sciences | 2006
Nicolas Ferlay; Harumi Isaka; Philip M. Gabriel; Albert Benassi
Abstract The multiresolution radiative transfer equations of Part I of this paper are solved numerically for the case of inhomogeneous model clouds using Meyer’s basis functions. After analyzing the properties of Meyer’s connection coefficients and effective coupling operators (ECOs) for two examples of extinction functions, the present approach is validated by comparisons with Spherical Harmonic Discrete Ordinate Method (SHDOM) and Monte Carlo codes, and a preliminary analysis of the local-scale coupling between the cloud inhomogeneities and the radiance fields is presented. It is demonstrated that the contribution of subpixel-scale cloud inhomogeneities to pixel-scale radiation fields may be very important and that it varies considerably as a function of local cloud inhomogeneities.