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Displaying similar documents to “Representations of isotropic Gaussian random fields with homogeneous increments.”

Properties of local-nondeterminism of Gaussian and stable random fields and their applications

Yimin Xiao (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of ( N , d ) -Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the...

Estimation of anisotropic gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2008)

ESAIM: Probability and Statistics

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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...

Invariance principle, multifractional gaussian processes and long-range dependence

Serge Cohen, Renaud Marty (2008)

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

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This paper is devoted to establish an invariance principle where the limit process is a multifractional gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional brownian motion.

Ordered random walks.

Eichelsbacher, Peter, König, Wolfgang (2008)

Electronic Journal of Probability [electronic only]

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