The system of singular-values of a square matrix whose components are independent Ornstein-Uhlenbeck processes corresponds to a diffusion model of interacting particles. We show that the weak limit, as the dimension of the matrix tends to infinity, of the associated empirical measure process is...

Moment inequalities for point process martingales are considered. Our main result is a point process analogue of Rosenthal's inequality for discrete-time martingales. It is also noted that this inequality generalises in a simple way to marked point process martingales.

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. points in , d[greater-or-equal, slanted]2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with...

Using bivariate Lévy processes, stationary and self-similar processes, with prescribed one-dimensional marginal laws of type G, are constructed. The self-similar processes are obtained from the stationary by the Lamperti transformation. In the case of square integrability the arbitrary spectral...

We consider statistical models for birth and death on a flow and prove local asymptotic normality as the observation time approaches infinity; as a consequence, we know how to characterize asymptotically efficient estimators for the unknown parameter. We construct a sequence of minimum distance...

The present article analyses the large-time behavior of a class of time-homogeneous diffusion processes whose spatially periodic dynamics, although time independent, involve a large spatial parameter 'a'. This leads to phase changes in the behavior of the process as time increases through...

Markov semigroups on the field of p-adic numbers which are symmetric with respect to a measure [rho](x) dx absolutely continuous relative to the Haar measure dx on are constructed. The corresponding Dirichlet forms and associated Markov processes are exhibited and shown to be of the jump type. A...

We compute the speed of convergence of the canonical Markov approximation of a chain with complete connections with summable decays. We show that in the -topology the approximation converges at least at a rate proportional to these decays. This is proven by explicitly constructing a coupling...

We consider a nearest-neighbor symmetric zero-range process, evolving on the d-dimensional periodic lattice, with a random jump rate and investigate its hydrodynamic behavior. We prove that the empirical distribution of particles converges in probability to the weak solution of the non-linear...