We consider a symmetric simple exclusion process on and obtain sharp estimates for the distribution of the first time the empirical density in a large box exceeds a given value larger than the initial density. As a corollary, we characterize the distribution of the process at this first...

Hidden Markov models (HMMs) have during the last decade become a widespread tool for modelling sequences of dependent random variables. In this paper we consider a recursive estimator for HMMs based on the m-dimensional distribution of the process and show that this estimator converges to the...

We consider the local empirical process indexed by sets, a substantial generalization of the well-studied uniform tail empirical process. We show that the weak limit of weighted versions of this process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main...

In this paper we study the existence of empirical distributions of G/G/1 queues via a sample-path approach. We show the convergence along a given trajectory of empirical distributions of the workload process of a G/G/1 queue under the condition that the work brought into the system has strictly...

We model the evolution of a single-species population by a size-dependent branching process Zt in discrete time. Given that Zt = n the expected value of Zt+1 may be written nexp(r - [gamma]n) where r 0 is a growth parameter and [gamma] 0 is an (inhibitive) environmental parameter. For small...

A multilevel bilinear system of stochastic differential equations is a multilevel mean field system in which the drift term is also linear. Two kinds of parameters coexist in this model: the rate of spatial mixing and the noise intensity. The parameter space is partitioned into three regions...

Consider the class of discrete time, general state space Markov chains which satisfy a "uniform ergodicity under sampling" condition. There are many ways to quantify the notion of "mixing time", i.e., time to approach stationarity from a worst initial state. We prove results asserting...

We study the existence and properties of the density for the law of the solution to a nonlinear hyperbolic stochastic partial differential equation, driven by a two-parameter white noise. We also analyze the asymptotic behavior of the density for the law of the solution to the equation obtained...

If a Markov chain satisfies a certain condition that is slightly weaker than [Psi]-mixing, then it also satisfies (with exponential mixing rate) the "interlaced [varrho]-mixing" condition.

We generalize a theorem of Köthe and Toeplitz on unconditional bases in Hilbert spaces to Hilbert space-valued measures. This leads to a necessary and sufficient condition for the completeness of the spectral domain of a weakly harmonizable process whose shift operator exists and is invertible....