A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion.
A different construction of gaussian fields from Markov chains : Dirichlet covariances
A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables.
A strong invariance principle for negatively associated random fields
In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite th moment and the covariance coefficient exponentially decreases to . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
A strong law of large numbers for harmonizable isotropic random fields.
A strong mixing condition for second-order stationary random fields
Let be a second-order stationary random field on Z². Let ℳ(L) be the linear span of , and ℳ(RN) the linear span of . Spectral criteria are given for the condition , where is the cosine of the angle between ℳ(L) and .
Aliasing in the sampling restoration of non-band-limited homogeneous random fields.
Almost Sure Sampling Reconstruction Of Non-Band-Limited Homogeneous Random Fields
An almost sure limit theorem for -mixing random fields.
An application of the nonselfadjoint operators theory in the study of stochastic processes.
Application du calcul de Malliavin aux équations différentielles stochastiques sur le plan
Application of the random field theory in PET imaging - injection dose optimization
This work presents new application of the random field theory in medical imaging. Results from both integral geometry and random field theory can be used to detect locations with significantly increased radiotracer uptake in images from positron emission tomography (PET). The assumptions needed to use these results are verified on a set of real and simulated phantom images. The proposed method of detecting activation (locations with increased radiotracer concentration) is used to quantify the quality...
Approximation in law to the d-parameter fractional Brownian sheet based on the functional invariance principle.
We show a result of approximation in law of the d-parameter fractional Brownian sheet in the space of the continuous functions on [0,T]d. The construction of these approximations is based on the functional invariance principle.
Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet
A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters Finally, the approximation process is iterative on the quarter plane A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2.
Argumentwise invariant kernels for the approximation of invariant functions
We consider the problem of designing adapted kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields with invariant paths, as well as Reproducing Kernel Hilbert Spaces of invariant functions. Two subclasses of argumentwise kernels are considered, involving a fundamental domain or a double sum over orbits. We then derive invariance properties...
Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ
We study the asymptotic behaviour, as n → ∞, of the Lebesgue measure of the set for a random k-dimensional subspace E ⊂ ℝⁿ and an isotropic convex body K ⊂ ℝⁿ. For k growing slowly to infinity, we prove it to be close to the suitably normalised Gaussian measure in of a t-dilate of the Euclidean unit ball. Some of the results hold for a wider class of probabilities on ℝⁿ.
Asymptotic growth of spatial derivatives of isotropic flows.
Asymptotic Rényi distances for random fields: properties and applications
The approach introduced in Janžura [Janzura 1997] is further developed and the asymptotic Rényi distances are studied mostly from the point of their monotonicity properties. The results are applied to the problems of statistical inference.
Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster
The aim of this paper is to extend the well-known asymptotic shape result for first-passage percolation on to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation model. We prove the convergence of the renormalized set of wet vertices to a deterministic shape that does not depend on the realization of the infinite cluster. As a special case of our result, we obtain an asymptotic shape theorem for the chemical distance in supercritical...
Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster
The aim of this paper is to extend the well-known asymptotic shape result for first-passage percolation on to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation model. We prove the convergence of the renormalized set of wet vertices to a deterministic shape that does not depend on the realization of the infinite cluster. As a special case of our result, we obtain an asymptotic shape theorem for the chemical distance in supercritical...