Anisotropic fractional Brownian fields: properties, simulation and estimation.

Abstract

In this talk, we focus on the anisotropic fractional Brownian field (AFBF), which is a multi-dimensional extension of the fractional Brownian motion. First, we define the field model and its two main functional parameters, namely the topothesy function and the Hurst function. We also present some heterogeneous extensions of this model known as anisotropic multifractional Brownian fields. We then describe their mathematical properties of models putting the emphasis on the assessment of their regularity and degree of anisotropy or heterogeneity. Next, we review methods for the estimation of model parameters and related features. In particular, we present methods based on quadratic variations for the estimation of model parameters and features. Eventually, we describe a simulation method based on turning-band fields that enables to sample realizations of AFBF.

Frédéric J.P. Richard

Professor of Applied Mathematics

Professor of applied mathematics whose research interests include image processing, spatial statistics and data science.