A natural approach to investigating the dynamics of stochastic flows is to study the action of such flows on measures. In models of pollution transport the resulting measure-valued random process describes the distribution of pollutant mass in space. When, in addition, pollutants are allowed to...

The rate of convergence (in the uniform Kolmogorov's distance) for probability distributions of parabolically rescaled solutions of the multidimensional Burgers' equation with random singular Gaussian initial data (with long-range dependence) to a limit Gaussian random field is discussed in this...

We prove a central limit theorem for the density field for stationary zero range processes in a random environment. We prove that the density field converges weakly to a generalized Ornstein-Uhlenbeck process whose evolution is described by the linearization of the hydrodynamic equation around a...

Randomly censored data consist of i.i.d. pairs of observations (Xi,[delta]i), i=1,...,n. If [delta]i=0, Xi denotes a censored observation, and if [delta]i=1, Xi denotes a survival time, which is the variable of interest. A popular stochastic measure of the distance between the density function f...

We consider an infinite particle system living on a torus; from the microscopic point of view, the particles move in a lattice and their evolution is described by a spatially inhomogeneous zero-range process: each particle jumps following a symmetric random walk, with rate depending on the...

This paper studies the Hausdorff dimensions of random non-self-similar fractals. Here, we obtain the Hausdorff dimensional estimates of random net fractals generated by random contractions (including random transformation contraction and random ratio contraction). In addition, we give the...

A new formulation of duality for pairs of stopping times is given. This formulation is constructive in that it provides a method for generating examples of dual times. We also use it to form the basis for a direct sample path proof of the Spitzer-Pollaczek factorization associated with a dual...

By the local time method we prove comparison theorems for systems of stochastic differential inequalities with respect to semimartingales. Furthermore, we construct the 'maximal/minimal solution' of a system of stochastic differential inequalities by the monotone iterative technique. In...

We study the Strassen's law of the iterated logarithm for diffusion processes for small values of the parameter. For the Brownian Motion this result can be obtained by time reversal, a technique which is not easy to reproduce for diffusion processes. A number of examples and applications are...

Asymptotic distributions for a family of time-varying symmetric statistics formed from an infinite particle system are derived and a representation for the limit is obtained in terms of multiple stochastic integrals. This family arises from a system of Brownian particles diffusing in R whose...