For a diffusion Xt in a one-dimensional Wiener medium W, it is known that there is a certain process (br(W))r=0 that depends only on the environment, so that Xt-blogt(W) converges in distribution as t--[infinity]. The paths of b are step functions. Denote by FX(t) the point with the most local...

A new method of estimation of intrinsic volume densities for a stationary random closed set with values in the extended convex ring is introduced. The local Steiner formula is applied to the closure of the complement of the [epsilon]-parallel set to [Xi] for n=d different radii and, by solving a...

We propose a class of polynomial birth-death point processes (abbreviated to PBDP) , where Z is a polynomial birth-death random variable defined in [T.C. Brown, A. Xia, Stein's method and birth-death processes, Ann. Probab. 29 (2001) 1373-1403], Ui's are independent and identically distributed...

A strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. The Razumikhin-Lyapunov type function methods and comparison principles are studied in pursuit of...

In the classical occupancy scheme, one considers a fixed discrete probability measure and throws balls independently at random in boxes labeled by , such that pi is the probability that a given ball falls into the box i. In this work, we are interested in asymptotic regimes of this scheme in the...

We study the exact asymptotics of , as u--[infinity], for centered Gaussian processes with the covariance function satisfying as h--0. The obtained results complement those already considered in the literature for the case of locally stationary Gaussian processes in the sense of Berman, where...

We consider a system of diffusing particles on the real line in a quadratic external potential and with a logarithmic interaction potential. The empirical measure process is known to converge weakly to a deterministic measure-valued process as the number of particles tends to infinity. Provided...

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck bridge connecting a given starting point x and an endpoint y provided y belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU...

We use the random self-similarity of the continuum random tree to show that it is homeomorphic to a post-critically finite self-similar fractal equipped with a random self-similar metric. As an application, we determine the mean and almost-sure leading order behaviour of the high frequency...

Besides fractional Brownian motion most non-Gaussian fractional fields are obtained by integration of deterministic kernels with respect to a random infinitely divisible measure. In this paper, generalized shot noise series are used to obtain approximations of most of these fractional fields,...