Anisotropic Analysis of Some Gaussian Models

By A. Bonami, Anne Estrade. 2003

185 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/b00537165ccb860b9585b4811e8cb31a209b3c95

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Citations in the corpus

Joint continuity of the local times of fractional Brownian sheets (2008, background): “These features of B make it a possible model for bone structure [8] and aquifer structure in hydrology [4].”
Sample Path Properties of Anisotropic Gaussian Random Fields (2009, background): “[10] and Bonami and Estrade [18] considered some anisotropic Gaussian random fields with stationary increments.”
Aquifer operator scaling and the effect on solute mixing and dispersion (2006, methodology): “Techniques have been developed that can handle this anisotropy in the scaling or the Hurst coefficients [Dobrushin, 1978; Hudson and Mason, 1982; Schertzer and Lovejoy, 1985, 1987; Kumar and Foufoula-Georgiou, 1993;Mason and Xiao, 2001;Bonami and Estrade, 2003] yet the mathematical character of nume”
Asymptotic Properties and Hausdorff Dimensions of Fractional Brownian Sheets (2005, unknown): “By examining the proofs, we see that Theorems 4, 5, and 6 hold for all Gaussian random fields satisfying (3.12) and (3.58), including certain anistropic Gaussian random fields with stationary increments (see e.g., Kôno [20], Bonami and Estrade [9, Example 3]).”
Geometric Properties of Fractional Brownian Sheets (2007, background): “The anisotropic property and the operator-self-similarity (1.6) of BH make it a possible model for bone structure [Bonami and Estrade (2003)] and aquifer structure in hydrology [Benson et al. (2004)].”
Sample path properties of bifractional Brownian motion (2006, unknown): “Many authors have also proposed using more general self-similar Gaussian processes and random fields as stochastic models (see, e.g., Addie et al. [1], Anh et al. [3], Benassi et al. [7], Mannersalo and Norros [30], Bonami and Estrade [12], Cheridito [13] and Benson et al. [8]).”
Hölder regularity for operator scaling stable random fields (2007, background): “However, certain applications (see, e.g., [5, 7] and references therein) require that the random (cid:12)eld is anisotropic and satis(cid:12)es a scaling relation.”
Operator scaling stable random fields (2006, methodology): “Many random fields occurring in applications have Hurst indices that vary with coordinate [7,8].”