The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time
series and spatial data. The graph of a smooth, differentiable surface indexed in ℝ d has …

We propose to compute a sparse approximate inverse Cholesky factor L of a dense
covariance matrix Θ by minimizing the Kullback--Leibler divergence between the Gaussian …

The simulation of random spatial data on a computer is an important tool for understanding
the behavior of spatial processes. In this chapter we describe how to simulate realizations …

Accurate description of the topography of active fault surfaces represents an important
geophysical issue because this topography is strongly related to the stress distribution along …

One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation
analysis (MFDFA) are widely used in the scaling analysis of fractal and multifractal time …

Understanding gas-magma dynamics in volcanic conduits and linking them with the
associated geophysical signals at the surface is of fundamental importance in monitoring …

Multifractal analysis is considered a promising tool for image processing, notably for texture
characterization. However, practical operational estimation procedures based on a …

This article proposes a new approach for Bayesian and maximum likelihood parameter
estimation for stationary Gaussian processes observed on a large lattice with missing …

This paper presents a new approach to the estimation of the deformation of an isotropic
Gaussian random field on ℝ2 based on dense observations of a single realization of the …

This volume is an attempt to provide a graduate level introduction to various aspects of
stochastic geometry, spatial statistics and random fields, with special emphasis placed on …