Estimating interactions in binary data sequences
Estimation of anisotropic gaussian fields through Radon transform
We estimate the anisotropic index of an anisotropic fractional brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional brownian field and prove that these processes admit...
Estimation of anisotropic Gaussian fields through Radon transform
We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes...
Estimation of the spectral density of a homogeneous random stable discrete time field.
In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discrete- time random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows can also be used to construct estimates of the spectral density of a homogeneous symmetric α-stable discrete-time random field. These fields do not have second-order moments if 0 < α < 2. We construct an estimate of the spectrum, calculate the asymptotic mean and variance,...
Exact rate of convergence for increments of random fields.
Exchanging the order of taking suprema and countable intersections of σ-algebras
Existence of moments of increasing predictable processes associated with one- and two-parameter potentials.
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients....
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. ...
Exponential inequalities for sums of weakly dependent variables.
Filtrage de diffusions bidirectionnelles pour une observation ponctuelle de Poisson à deux paramètres
Flots browniens isotropes sur la sphère
From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields
Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. In the case of multiparameter Gaussian random fields, Adler proved that these two concepts are connected under the assumption of increment stationarity property. The aim of this paper is to consider the case of Gaussian fields without any stationarity condition. More precisely, we prove that almost surely the Hausdorff dimensions of the range and the graph...
Functionals associated with self-intersections of the planar brownian motion
Generalized madogram and pairwise dependence of maxima over two regions of a random field
Spatial environmental processes often exhibit dependence in their large values. In order to model such processes their dependence properties must be characterized and quantified. In this paper we introduce a measure that evaluates the dependence among extreme observations located in two disjoint sets of locations of . We compute the range of this new dependence measure, which extends the existing -madogram concept, and compare it with extremal coefficients, finding generalizations of the known...
Hausdorff dimension of the graph of the fractional Brownian sheet.
Heat kernel measure on central extension of current groups in any dimension.
Hierarchical equilibria of branching populations.
Images of Gaussian random fields: Salem sets and interior points
Let be a Gaussian random field in with stationary increments. For any Borel set , we provide sufficient conditions for the image X(E) to be a Salem set or to have interior points by studying the asymptotic properties of the Fourier transform of the occupation measure of X and the continuity of the local times of X on E, respectively. Our results extend and improve the previous theorems of Pitt [24] and Kahane [12,13] for fractional Brownian motion.
Inégalités relatives aux processus d’Ornstein-Uhlenbeck à paramètres et capacité gaussienne