— Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term… (More)

In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given σ-field Q. In our framework, we recall well-known results about… (More)

We address the issue of estimating the regression vector β in the generic s-sparse linear model y = Xβ + z, with β ∈ ℝ<sup>p</sup>, y ∈ ℝ<sup>n</sup>, z ~ )V (0, σ<sup>2</sup>I), and p > n when the… (More)

By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm), and should… (More)

We study the dynamical properties of the Brownian diffusions having σ Id as diffusion coefficient matrix and b = ∇U as drift vector. We characterize this class through the equality D + = D 2 −, where… (More)

Asymptotic expansions at any time for scalar fractional SDEs with Hurst index H > 1/2 SÉBASTIEN DARSES and IVAN NOURDIN Boston University, Department of Mathematics and Statistics, 111 Cummington… (More)

In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given σ-field Q. In our framework, we recall well-known results about Markov… (More)

In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given σ-field Q. In our framework, we recall well-known results about Markov… (More)

— We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an… (More)