Entropy numbers of certain summation operators.
Enveloppes convexes des processus gaussiens
Equivalence of Gaussian measures of finite sum of stochastic processes
Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion
A linear-quadratic control problem with an infinite time horizon for some infinite dimensional controlled stochastic differential equations driven by a fractional Brownian motion is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well known linear feedback control for the associated infinite dimensional deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system...
Erratum to “Number variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric -stable processes".
Espaces de Fock pour les processus de Wiener et de Poisson
Estimation in models driven by fractional brownian motion
Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ x and μ(x)=μ or μ(x)=μ x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...
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 moment by means of the extrema.
An estimator of the standard deviation of the first derivative of a stationary Gaussian process with known variance and two continuous derivatives, based on the values of the relative maxima and minima, is proposed, and some of its properties are considered.
Every continuous first order autoregressive stochastic process is a Gaussian process
Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in with non-zero mean.
Expansions for Gaussian processes and Parseval frames.
Exponentielles et fonctionnelles de Schwinger en analyse gaussienne non commutative
Extremes in multivariate stationary normal sequences
This paper deals with a weak convergence of maximum vectors built on the base of stationary and normal sequences of relatively strongly dependent random vectors. The discussion concentrates on the normality of limits and extends some results of McCormick and Mittal [4] to the multivariate case.
Fast sets and points for fractional brownian motion
Feynman-Kac formula, λ-Poisson kernels and λ-Green functions of half-spaces and balls in hyperbolic spaces
We apply the Feynman-Kac formula to compute the λ-Poisson kernels and λ-Green functions for half-spaces or balls in hyperbolic spaces. We present known results in a unified way and also provide new formulas for the λ-Poisson kernels and λ-Green functions of half-spaces in ℍⁿ and for balls in real and complex hyperbolic spaces.
Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case
Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of , where , i = 1,...,n, are independent fractional Brownian motions with Hurst parameters and λ₁,...,λₙ > 0. The asymptotics takes one of three different qualitative forms, depending on the value of .
Fonctions aléatoires gaussiennes, les résultats récents de M. Talagrand
Fonctions de Young et continuité des trajectoires d'une fonction aléatoire
À l’aide des notions de fonctions de Young et d’entropie métrique, nous donnons des conditions suffisantes d’existence d’une version à trajectoires continues et nous déterminons des modules de continuité uniforme pour les trajectoires de cette version dans des cas plus généraux que les fonctions aléatoires réelles gaussiennes.