Publication

Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields

Publications associées (17)

Moments And Growth Indices For The Nonlinear Stochastic Heat Equation With Rough Initial Conditions

We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but th ...

Inst Mathematical Statistics2015

Feynman-Kac representation for the parabolic Anderson model driven by fractional noise

Thomas Mountford, Kamran Kalbasi

We consider the parabolic Anderson model driven by fractional noise: partial derivative/partial derivative t u(t,x) = k Delta u(t,x) + u(t,x)partial derivative/partial derivative t W(t,x) x is an element of Z(d), t >= 0, where k > 0 is a diffusion constant ...

Academic Press Inc Elsevier Science2015

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Michaël Unser, Arash Amini, Pouya Dehghani Tafti, Hagay Kirshner

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

Yuri Faenza, Hans Raj Tiwary

We show that the binary logarithm of the nonnegative rank of a nonnegative matrix is, up to small constants, equal to the minimum complexity of a randomized communication protocol computing the matrix in expectation. We use this connection to prove new con ...

Springer Berlin Heidelberg2012

Stochastic Models for Sparse and Piecewise-Smooth Signals

Michaël Unser, Pouya Dehghani Tafti

We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is ana ...

IEEE2011

Propriétés fines des trajectoires du mouvement brownien fractionnaire

Driss Baraka

Let X = {X(t); t ∈ RN} be a (N,d) fractional Brownian motion in Rd of index H ∈ (0,1). We study the local time of X for all temporal dimensions N and spatial dimensions d for which local time exist. We obtain two main results : R1. If we denote by Lx(I) th ...

EPFL2008

A law of the iterated logarithm for fractional Brownian motions

Thomas Mountford, Driss Baraka

We show that for a class of Gaussian processes indexed by one dimensional time, the local times obey the behavior conjectured by Xiao. ...

2008