In this paper we investigate the cluster behavior of linearly interacting Brownian motions indexed by . We show that (on a logarithmic scale) the block average process converges in path space to Brownian motion.

We construct a catalytic super process X (measure-valued spatial branching process) where the local branching rate is governed by an additive functional A of the motion process. These processes have been investigated before but under restrictive assumptions on A. Here we do not even need...

Classical super-Brownian motion (SBM) is known to take values in the space of absolutely continuous measures only if d=1. For d[greater-or-equal, slanted]2 its values are almost surely singular with respect to Lebesgue measure. This result has been generalized to more general motion laws and...

A strong law of large numbers is presented for a class of random variables X0, X1,..., which satisfy for a suitable function [latin small letter f with hook](x) > x.

We study asymptotic properties of non-negative random variables Xn, n[greater-or-equal, slanted]0, satisfying the recursion . If the functions g(x) and [sigma]2(x) are properly balanced at infinity, Xn is asymptotically [Gamma]-distributed in a suitable scale. This result contains several known...

We generalize a result by Kozlov on large deviations of branching processes (Zn) in an i.i.d. random environment. Under the assumption that the offspring distributions have geometrically bounded tails and mild regularity of the associated random walk S, the asymptotics of is (on logarithmic...

The asymptotic normality of U-statistics has so far been proved for iid data and under various mixing conditions such as absolute regularity, but not for strong mixing. We use a coupling technique introduced in 1983 by Bradley [R.C. Bradley, Approximation theorems for strongly mixing random...

In this paper we compute large deviation probabilities for two classes of weakly dependent processes, moving averages of i.i.d. random variables and Poisson center cluster random measures.

Let (Xi)[infinity]i = 1 be a stationary, mean-zero Gaussian process with covariances r(k) = EXk + 1 X1 satisfying r(0) = 1 and r(k) = k-DL(k). Consider the two-parameter empirical process for G(Xi), where G is any measurable function. The Functional Law of the Iterated Logarithm as well as a...