The hydrodynamic limit of the symmetric generalized exclusion process on the torus [0,1) has previously been proved to be a nonlinear diffusive equation. We consider in this paper this model in infinite volume. We prove that the H-1 norm of the difference between the process and the solution of...

We provide an example of a class of partial differential equations being stabilized (in terms of Lyapunov exponents) by noise. In particular, we show that the stability of the heat equation can be improved by adding a stochastic term to the equation. We also give an example of an unstable PDE...

Consider a sum of Markov dependent lattice variables. The normal approximation is trivial for this sum if the total variation distance is considered. Replacement of the normal approximation by its Poisson structured analogue changes the situation radically. Moreover, considering the Markov...

Periodic ARMA, or PARMA, time series are used to model periodically stationary time series. In this paper we develop the innovations algorithm for periodically stationary processes. We then show how the algorithm can be used to obtain parameter estimates for the PARMA model. These estimates are...

In many applications of Markov chains, and especially in Markov chain Monte Carlo algorithms, the rate of convergence of the chain is of critical importance. Most techniques to establish such rates require bounds on the distribution of the random regeneration time T that can be constructed, via...

We present, in discrete time, general-state-space dualities between content and insurance risk processes that generalize the stationary recursive duality of Asmussen and Sigman (1996, Probab. Eng. Inf. Sci. 10, 1-20) and the Markovian duality of Siegmund (1976, Ann. Probab. 4, 914-924) (both of...

We investigate existence of an invariant probability measure for the equation in a conuclear space [Phi]', where W is a Wiener process in [Phi]' and generates a semigroup in [Phi]. In the first part of the paper we formulate a sufficient and necessary condition for the existence of an invariant...

Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential equations are shown in this paper. In particular, the main results obtained in Caraballo and Real (1994, Stochast. Anal. Appl. 12(5), 517-525) are improved, since the new...

We study the structure of point processes N with the property that the vary in a finite-dimensional space where [theta]t is the shift and the [sigma]-field generated by the counting process up to time t. This class of point processes is strictly larger than Neuts' class of Markovian arrival...

This paper deals with the study of the relationship between the complete linear regularity of continuous-time weakly stationary processes and the smoothness of their spectral densities. It is shown that when the coefficient of complete linear regularity behaves like O([tau]-(r+[mu])) as [tau] --...