We study an infinite system of Brownian hard balls, moving in and submitted to a smooth infinite range pair potential. It is represented by a diffusion process, which is constructed as the unique strong solution of an infinite-dimensional Skorohod equation. We also prove that canonical Gibbs...

Suppose that f is a deterministic function, is a sequence of random variables with long-range dependence and BH is a fractional Brownian motion (fBm) with index . In this work, we provide sufficient conditions for the convergencein distribution, as m--[infinity]. We also consider two examples....

Let 0<[alpha][less-than-or-equals, slant]2 and let . Let {X(t),t[set membership, variant]T} be a linear fractional [alpha]-stable (0<[alpha][less-than-or-equals, slant]2) motion with scaling index H (0<H<1) and with symmetric [alpha]-stable random measure. Suppose that [psi] is a bounded real function with compact support [a,b] and at least one null moment. Let the sequence of the discrete wavelet coefficients of the process X beWe use a stochastic integral representation of the process X to describe the wavelet coefficients as [alpha]-stable integrals when H-1/[alpha]>-1. This stochastic representation is used to prove that the stochastic process of wavelet coefficients , with fixed scale index , is strictly stationary. Furthermore, a property of self-similarity of the wavelet coefficients of X is proved. This property has been the motivation of several...</[alpha][less-than-or-equals,>

The stochastic delay differential equationis considered, where Z(t) is a process with independent stationary increments and a is a finite signed measure. We obtain necessary and sufficient conditions for the existence of a stationary solution to this equation in terms of a and the Lévy measure...

Consider a class of diffusions with random potentials which behave asymptotically as Brownian motion. We study the tightness of localization around the bottom of some Brownian valley, and determine the limit distribution of the return time to the origin after a typical time. Via the Skorokhod...

Traditional methods of estimating frequencies of sinusoids from noisy data include periodogram maximization and nonlinear least squares, which lead to efficient estimates with the rate . To actually compute these estimates, some iterative search procedures have to be employed because of the high...

Consider the finite measure-valued continuous super-Brownian motion X on corresponding to the log-Laplace equation where the coefficient [beta](x) for the additional mass production varies in space, is Hölder continuous, and bounded from above. We prove criteria for (finite time) extinction and...

A large deviation principle is established for stochastic differential equation systems with slow and fast components and small diffusions in the slow component.

The paper examines multiplicative ergodic theorems and the related multiplicative Poisson equation for an irreducible Markov chain on a countable state space. The partial products are considered for a real-valued function on the state space. If the function of interest satisfies a monotone...

In this paper we investigate the almost sure ('quenched') asymptotics for a Brownian traveller, moving on the Sierpinski gasket with Poisson-type attracting potential interaction. The quenched behaviour is different from the 'annealed' one (averaged with respect to the random potential).