The paper is concerned with the heat equation perturbed by a spatially homogeneous Wiener process. It is shown, under general conditions on the spectral density of the noise, that solutions starting from non-negative initial conditions are strictly positive for all positive times. The result has...

For a stable subordinator Yt of index [alpha], 0<[alpha]<1, the occupation measure[mu](A)={t[set membership, variant][0,1] : Yt[set membership, variant]A}is known to have (with probability 1) the property thatIn order to obtain an interesting spectrum for the large values of [mu](x-r,x+r), we consider the setwhere c[alpha] is a suitable constant. It is shown that B[theta]=[empty set][combining character] for [theta]>1, and B[theta] [not equal to] [empty set][combining character] for 0[less-than-or-equals, slant][theta][less-than-or-equals, slant]1; moreover, dim B[theta]=Dim B[theta]=[alpha](1-[theta]1/(1-[alpha])).

We consider a parallel simulated annealing algorithm that is closely related to the so-called parallel chain algorithm. Periodically a new state from states is chosen as the initial state for simulated annealing Markov chains running independent of each other. We use selection strategies such as...

Some "classical" stochastic differential equations have been used in the theory of measurements continuous in time in quantum mechanics and, more generally, in quantum open system theory. In this paper, we introduce and study a class of such equations which allow us to achieve the same level of...

An analogue of the Lindley equation for random walk is studied in the context of the branching random walk, taking up the studies of Karpelevich, Kelbert and Suhov [(1993a) In: Boccara, N., Goles, E., Martinez, S., Picco, P. (Eds.), Cellular Automata and Cooperative Behaviour. Kluwer, Dordrecht,...

In this paper, a class of Gaussian processes, having locally the same fractal properties as fractional Brownian motion, is studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. A time dependency of the integrand of the classical Wiener...

Let [phi] be a Hausdorff measure function and let [Lambda] be an infinite increasing sequence of positive integers. The Hausdorff-type measure [phi]-m[Lambda] associated to [phi] and [Lambda] is studied. Let be fractional Brownian motion of index [alpha] in We evaluate the exact [phi]-m[Lambda]...

It is shown that the Gibbs probability measure of the SOS model transformed by reducing the level-variables under the sign-map provides an example of a non-Gibbsian measure. The persistence of non-Gibbsianness under some transformations is discussed.

Consider the class of n-stage decision models with state space S, action space A, and payoff function g : (S x A)n x S -- R. The function g is Markov-achievable if for any possible set of available randomized actions and all transition laws, each plan has a corresponding Markov plan whose value...

We investigate the question of when sampling a stochastic process X={X(t): t[greater-or-equal, slanted]0} at the times of an independent point process [psi] leads to the same empirical distribution as the time-average limiting distribution of X. Two main cases are considered. The first is...