We prove a conditioned version of the ergodic theorem for Markov processes, which we call a quasi-ergodic theorem. We also prove a convergence result for conditioned processes as the conditioning event becomes rarer.

The thermodynamic limit of a classical mean field system perturbed by a small Sherrington-Kirkpatrick term is derived. It is proved to exhibit behaviors that may strongly differ from the usual ones. Examples are given showing that every situation is likely to occur. The main tools that are used...

In this paper we study Varadhan's estimates for the density of a family of solutions of anticipating stochastic differential equations driven by a white noise which is perturbed by a small parameter [var epsilon]. The anticipating input is given by the initial condition and the stochastic...

We provide a general comparison theorem for systems of stochastic partial differential equations, which is a powerful tool to study stability as well as stochastic invariance of the corresponding solution processes. An application showing stability properties of a predator-prey system is given.

In this paper, we investigate the regularity of the solutions of a class of two-parameter Stochastic Volterra-type equations in the anisotropic Besov-Orlicz space modulated by the Young function [tau](t)=exp(t2)-1 and the modulus of continuity [omega](t)=(t(1+log(1/t)))1/2. Moreover, we derive...

In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter point process into a planar Poisson process of unit rate, using random stopping sets. Merzbach and Nualart's theorem applies only to a special class of point processes, since it requires two restrictive...

In this paper we prove exponential asymptotic stability for discrete-time filters for signals arising as solutions of d-dimensional stochastic difference equations. The observation process is the signal corrupted by an additive white noise of sufficiently small variance. The model for the signal...

In this work we study limit theorems for the Hopf-Cole solution of the Burgers equation when the initial value is a functional of some Gaussian processes. We use the Gaussian chaos decomposition, and we get "Gaussian scenario" with new normalization factors.

In this paper moving-average processes with no parametric assumption on the error distribution are considered. A new convolution-type estimator of the marginal density of a MA(1) is presented. This estimator is closely related to some previous ones used to estimate the integrated squared density...

A Moderate Deviation Principle is established for random processes arising as small random perturbations of one-dimensional dynamical systems of the form Xn=f(Xn-1). Unlike in the Large Deviations Theory the resulting rate function is independent of the underlying noise distribution, and is...