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Images of Gaussian random fields: Salem sets and interior points

Narn-Rueih Shieh, Yimin Xiao (2006)

Studia Mathematica

Let $X = X (t), t \in ℝ^{N}$ be a Gaussian random field in $ℝ^{d}$ with stationary increments. For any Borel set $E \subset ℝ^{N}$ , 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 $n$ paramètres et capacité gaussienne $c_{n, 2}$

Shiqi Song (1993)

Séminaire de probabilités de Strasbourg

Interacting brownian particles and Gibbs fields on pathspaces

David Dereudre (2003)

ESAIM: Probability and Statistics

In this paper, we prove that the laws of interacting brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Interacting Brownian particles and Gibbs fields on pathspaces

David Dereudre (2010)

ESAIM: Probability and Statistics

In this paper, we prove that the laws of interacting Brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of Hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to Brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Invariant random fields in vector bundles and application to cosmology

Anatoliy Malyarenko (2011)

Annales de l'I.H.P. Probabilités et statistiques

We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group G is obtained. We discuss an application to the theory of relic radiation, where G = SO(3). A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.

Isotropy of stationary random fields on lattice

Antonín Otáhal (1986)

Kybernetika