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Enhanced Gaussian processes and applications

Laure Coutin, Nicolas Victoir (2009)

ESAIM: Probability and Statistics

We propose some construction of enhanced Gaussian processes using Karhunen-Loeve expansion. We obtain a characterization and some criterion of existence and uniqueness. Using rough-path theory, we derive some Wong-Zakai Theorem.

Estimation of anisotropic gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2008)

ESAIM: Probability and Statistics

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

Hermine Biermé, Frédéric Richard (2007)

ESAIM: Probability and Statistics

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...

Existence and asymptotic behaviour of some time-inhomogeneous diffusions

Mihai Gradinaru, Yoann Offret (2013)

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

Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient ρ sgn ( x ) | x | α / t β . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters ρ , α and β , of the recurrence, transience and convergence. More precisely, asymptotic...

Existence et régularité höldérienne des fonctions de bosses

Moez Ben Abid (2009)

Colloquium Mathematicae

We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.

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