We study the equivalence of ensembles for stationary measures of interacting particle systems with two conserved quantities and unbounded local state space. The main motivation is a condensation transition in the zero-range process which has recently attracted attention. Establishing the...

A representation of the potential operator of an absorbing Lévy process in the half space , is given in terms of three measures and on arising in the fluctuation theory of Lévy processes. In the case of a rotation invariant stable Lévy process, the potential kernel in the half space is...

We study absolute-continuity relationships for a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to the law of the original process and we compute...

A stochastic version of modified Navier-Stokes equations (introduced by Prouse) is considered in a three-dimensional torus; its main feature is that instead of the linear term -[nu][big up triangle, open]u of the Navier-Stokes equations there is a nonlinear term . First, for this equation we...

Let M be a purely discontinuous martingale relative to a filtration . Given an arbitrary extension of the filtration , we will provide sufficient conditions for M to be a semimartingale relative to . Moreover we describe methods of how to find the Doob-Meyer decomposition with respect to the...

We consider a nonparametric estimation problem for the Lévy measure of time-inhomogeneous process with independent increments. We derive the functional asymptotic normality and efficiency, in an l[infinity]-space, of generalized Nelson-Aalen estimators. Also we propose some asymptotically...

This paper deals with the splitting method first introduced in rare event analysis. In this technique, the sample paths are split into R multiple copies at various stages during the simulation. Given the cost, the optimization of the algorithm suggests sampling a number of subtrials which may be...

We propose a set-indexed family of capacities on the classical Wiener space . This family interpolates between the Wiener measure () on and the standard capacity () on Wiener space. We then apply our capacities to characterize all quasi-sure lower functions in . In order to do this we derive the...

A general notion of canonical correlation is developed that extends the classical multivariate concept to include function-valued random elements X and Y. The approach is based on the polar representation of a particular linear operator defined on reproducing kernel Hilbert spaces corresponding...

In this paper we study the continuity property as well as the homeomorphism property for the solutions of multidimensional stochastic differential equations with jumps and non-Lipschitz coefficients with respect to the initial values.