We consider dissipative systems resulting from the Gaussian and alpha-stable noise perturbations of measure-preserving maps on the d dimensional torus. We study the dissipation time scale and its physical implications as the noise level ε vanishes. We show that nonergodic maps give rise to an O(1/ε) dissipation time whereas ergodic toral automorphisms, including cat maps and their d-dimensional...

We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is the KPP type nonlinearity. For a stationary and ergodic medium, and for certain initial condition, the solution develops a moving front that has a deterministic asymptotic speed in the large time limit. The main result of this articl...

Consider the Wonham optimal filtering problem for a finite state ergodic Markov process in both discrete and continuous time, and let σ be the noise intensity for the observation. We examine the sensitivity of the solution with respect to the filter’s initial conditions in terms of the gap between the first two Lyapunov exponents of the Zakai equation for the unnormalized conditional probabilit...

We study the relative impact of small-scale random inhomogeneities and singular perturbations in nonlinear elasticity. More precisely, we analyse the asymptotic behaviour of the energy functionals Fε(ω)(u) = ∫ A ( f ( ω, x ε ,Du ) + ε|∆u| ) dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic properties of the body. For f stati...

We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control problems introduced in [6]. We prove that, as time horizon goes to infinity (resp. discount factor goes to zero) the long run average solution to the parabolic system (resp. the limiting discounted solution to the ellip...

This article proposes a Bayesian infinite mixture model for the estimation of the conditional density of an ergodic time series. A nonparametric prior on the conditional density is described through the Dirichlet process. In the mixture model, a kernel is used leading to a dynamic nonlinear autoregressivemodel. This model can approximate any linear autoregressivemodel arbitrarily closely while ...

Dielectric nonlinear response of (PbMg1/3Nb2/3O3)0.9(PbTiO3)0.1 (0.9PMN0.1PT) relaxor ceramics was investigated under different ac drive voltages. It was observed that: (i) the dielectric permittivity is independent on ac field amplitude at high temperatures; (ii) with increasing ac drive, the permittivity maximum increases, and the temperature of the maximum shifts to lower temperature; (iii) ...

The analysis of economic time series is central to a wide range of applications, including business cycle measurement, financial risk management, policy analysis based on structural dynamic econometric models, and forecasting. This article provides an overview of the problems of specification, estimation and inference in linear stationary and ergodic time series models as well as non-stationary...

In this note we prove the stochastic homogenization for a large class of fully nonlinear elliptic integro-differential equations in stationary ergodic random environments. Such equations include, but are not limited to Bellman equations and the Isaacs equations for the control and differential games of some pure jump processes in a random, rapidly varying environment. The translation invariant ...

Viscosity solutions methods are used to pass to the limit in some penalization problems for rst order and second order, degenerate parabolic, Hamilton-Jacobi-Bellman equations. This characterizes the limit of the value functions of singularly perturbed optimal control problems for nonlinear deterministic systems and controlled degenerate diiusions, respectively. The results cover also cases whe...