We study the asymptotic behaviour of the occupation time process [integral operator]t0 IA(W1(L2(s)))ds, t [greater-or-equal, slanted] 0, where W1 is a standard Wiener process and L2 is a Wiener local time process at zero that is independent from W1. We prove limit laws, as well as almost sure...

This paper deals with characterizations for the distributional regeneration of general Markov chains. In particular, we formulate sufficient conditions for the positive recurrence in terms of matrix representations and minorization conditions. As examples we study the distributional regeneration...

Consider an ordinary Boolean model, that is, a homogeneous Poisson point process in Rd, where the points are all centres of random balls with i.i.d. radii. Now let these points move around according to i.i.d. stochastic processes. It is not hard to show that at each fixed time t we again have a...

A Poisson process in space-time is used to generate a linear Kolmogorov's birth-growth model. Points start to form on [0,L] at time zero. Each newly formed point initiates two bidirectional moving frontiers of constant speed. New points continue to form on not-yet passed over parts of [0,L]. The...

Let Sn, n [greater-or-equal, slanted] 1, be the partial sums of i.i.d. random variables with negative mean value. Many papers (see, for example, [1,2,5,6,7,9,11]) give us different theorems on the tail behavior of the distribution of sup {Sn,n [greater-or-equal, slanted] 1}. In this paper the...

We consider a modification of the well-known system of coalescing random walks in one dimension, both in discrete and continuous time. In our models each particle moves with unit speed, and it can change its direction of movement only at times of collisions with other particles. At these times...

This work considers the approach to stationarity of a Markov process of birth and death on stochastic flows. The process takes values in the space of counting measures, so its stationary states are point processes representing equilibrium distributions of points of unit mass. Stationary states...

We study the positive solutions of a heat equation on an infinite-dimensional state space using Hida's white noise analysis. We establish an integral representation theorem for generalized parabolic functions via so-called generalized Cameron-Martin densities, and we apply the representation...

The Fourier analytic approach due to S.M. Berman is considered for a certain class of [alpha]-stable moving average processes, 1 [alpha] = 2. It is proved that the local times of such processes satisfy a uniform Hölder condition of order Q1 - 1/[alpha] logQ1/[alpha] for small intervals Q. A...

In this paper some properties of the correlation autoregressive (CAR) sequences are studied. A representation for the correlation function of an arbitrary CAR sequence is obtained and the relationship between a CAR equation and the growth of the variance and location of spectral lines is...