We prove existence of a wetting transition for two classes of gradient fields which include: (1) The Continuous SOS model in any dimension and (2) The massless Gaussian model in dimension 2. Combined with a recent result proving the absence of such a transition for Gaussian models above 2...

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate [alpha]j. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of...

We investigate the extremal behavior of a special class of autoregressive processes with ARCH(1) errors given by the stochastic difference equationwhere are i.i.d. random variables. The extremes of such processes occur typically in clusters. We give an explicit formula for the extremal index and...

Using Stein's method, assuming Lindeberg's condition, we find a necessary and sufficient condition for the central limit theorem to hold for an array of random variables such that the variables in each row are negatively correlated (i.e., every pair has negative covariance) and their squares are...

In this paper we derive conditions for geometric ergodicity of the random-walk-based Metropolis algorithm on . We show that at least exponentially light tails of the target density is a necessity. This extends the one-dimensional result of Mengersen and Tweedie (1996, Ann. Statist. 24, 101-121)....

We pursue the investigation started in a recent paper by Millet and Sanz-Solé (1999, Ann. Probab. 27, 803-844) concerning a non-linear wave equation driven by a Gaussian white noise in time and correlated in the two-dimensional space variable. Under more restrictive conditions on the covariance...

We find a dimension function [phi]* such that the [phi]*-packing measure of the boundary of a Galton-Watson tree is strictly positive and finite.

We consider partial sums of i.i.d. random variables with moments E(X1)=0, E(X12)=[sigma]2 and and show thatwith some explicit function [phi](·). A related result for random variables with exponentially thin tails has recently been shown by Steinebach, extending a result given by Shao.

The only normal martingales which posses the chaotic representation property and the weaker predictable representation property and which are at the same time also Lévy processes, are in essence Brownian motion and the compensated Poisson process. For a general Lévy process (satisfying some...

A class of systems of infinite horizon forward-backward stochastic differential equations is investigated. Under some monotonicity assumptions, the existence and uniqueness results are established by means of a homotopy method. The global exponential asymptotical stability is also obtained. A...