A semilinear parabolic equation on d with a non-additive random perturbation is studied. The noise is supposed to be a spatially homogeneous Wiener process. Conditions for the existence and uniqueness of the solution in terms of the spectral measure of the noise are given. Applications to...

Let X be a linear process having a finite fourth moment. Assume is a class of square-integrable functions. We consider the empirical spectral distribution function Jn,X based on X and indexed by . If is totally bounded then Jn,X satisfies a uniform strong law of large numbers. If, in addition, a...

We extend Föllmer's results on time reversal on Wiener space to the case of some reflected diffusions.

This paper establishes the consistency and the root-n asymptotic normality of the exact maximum likelihood estimator of the dependence parameter in linear regression models where the errors are a nondecreasing function of a long-range-dependent stationary Gaussian process. The spectral density...

The collective epidemic model is a quite flexible model that describes the spread of an infectious disease of the Susceptible-Infected-Removed type in a closed population. A statistic of great interest is the final number of susceptibles who survive the disease. In the present paper, a necessary...

Let X be a stable subordinator of index [alpha] and [mu] be the occupation measure of X. Denote d([mu],x) and as the lower and upper local dimensions of [mu]. We obtain that the Hausdorff dimension of the set of the points where is (2[alpha]2/[beta]) - [alpha] a.s. and the lower bound of packing...

The porous medium equation on a d-dimensional torus is obtained as a hydrodynamic scaling limit, with the usual diffusion scaling, of the empirical measures of a sequence of reversible Markov jump processes on approximating periodic lattices. Each process can be viewed as a randomly interacting...

We consider a Gaussian process X with smoothness comparable to the Brownian motion. We analyze reconstructions of X which are based on observations at finitely many points. For each realization of X the error is defined in a weighted supremum norm; the overall error of a reconstruction is...

Recently, N. Kôno gave a limit theorem for occupation times of fractional Brownian motion, which result generalizes the well-known Kallianpur-Robbins law for two-dimensional Brownian motion. This paper studies a functional limit theorem for Kôno's result. It is proved that, under a suitable...