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We introduce a stochastic model to analyze in quantitative detail the effect of the high frequency components of the residual accelerations onboard spacecraft (often called g-jitter) on fluid motion. The residual acceleration field is…
The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
We address the problem of modulating a parameter onto a power-limited signal, transmitted over a discrete-time Gaussian channel and estimating this parameter at the receiver. Continuing an earlier work, where the optimal trade-off between…
This paper investigates a damped stochastic wave equation driven by a non-Gaussian Levy noise. The weak solution is proved to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition…
We consider a non-linear stochastic wave equation driven by space-time white noise in dimension 1. First of all, we state some results about the intermittency of the solution, which have only been carefully studied in some particular cases…
We consider a general class of SPDEs in $\mathbb{R}^d$ driven by a Gaussian spatially homogeneous noise which is white in time. We provide sufficient conditions on the coefficients and the spectral measure associated to the noise ensuring…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…
The problem of parameter estimation by the observations of the two-state telegraph process in the presence of white Gaussian noise is considered. The properties of estimator of the method of moments are described in the asymptotics of large…
High-quality nanomechanical oscillators can sensitively probe force, mass, or displacement in experiments bridging the gap between the classical and quantum domain. Dynamics of these stochastic systems is inherently determined by the…
We investigate instabilities in a stochastic mathematical model of cochlear dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators, together with the cochlear…
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…
Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations.…
The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes…
System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case,…
In this paper, we discuss an initial boundary value problem for the stochastic wave equation involving the nonlinear damping term $|u_t|^{q-2}u_t$ and a source term of the type $|u|^{p-2}u$. We firstly establish the local existence and…