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The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
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…
This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…
In this article, we study the stochastic wave equation in all dimensions $d\leq 3$, driven by a Gaussian noise $\dot{W}$ which does not depend on time. We assume that either the noise is white, or the covariance function of the noise…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
We consider the problem of frequency estimation of the periodic signal multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We show the consistency and asymptotic…
This paper deals with linear stochastic partial differential equations with variable coefficients driven by L\'{e}vy white noise. We first derive an existence theorem for integral transforms of L\'{e}vy white noise and prove the existence…
Asymptotic energy-distortion performance of zero-delay communication scenarios under additive white Gaussian noise is investigated. Using high-resolution analysis for quantizer design, the higher-order term in the logarithm of the…
In this paper, we consider an inference problem for the first order autoregressive process driven by a long memory stationary Gaussian process. Suppose that the covariance function of the noise can be expressed as $\abs{k}^{2H-2}$ times a…
In this paper, we consider a stochastic model of incompressible second grade fluids on a bounded domain of R^2 driven by linear multiplicative Brownian noise with anticipating initial conditions. The existence and uniqueness of the…
We study the well solvability of nonlinear backward stochastic evolutionary equations driven by a space-time white noise. We first establish a novel a priori estimate for solution of linear backward stochastic evolutionary equations, and…
We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…
This paper considers uncertainty quantification in systems perturbed by stochastic disturbances, in particular, Gaussian white noise. The main focus of this work is on describing the time evolution of statistical moments of certain…
Instead of a continuous system driven by Gaussian white noise, logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise, which shows a phenomenon different from…
We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper [K.…
This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is…
White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…