Extreme values of a stationary, multivariate time series may exhibit dependence across coordinates and over time. The aim of this paper is to offer a new and potentially useful tool called tail process to describe and model such extremes. The key property is the following fact: existence of the...

We study the asymptotic behaviour of the empirical distribution function derived from a stationary marked point process when a convex sampling window is expanding without bounds in all directions. We consider a random field model which assumes that the marks and the points are independent...

In this paper, we study nonparametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations with step [Delta]. The asymptotic framework is: n tends to infinity, [Delta]=[Delta]n tends to zero while n[Delta]n tends to infinity. First, we use a...

The Smoluchowski equations are a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers or by positive reals, these corresponding to the discrete or the...

Let M=(Mt)t=0 be any continuous real-valued stochastic process. We prove that if there exists a sequence (an)n=1 of real numbers which converges to 0 and such that M satisfies the reflection property at all levels an and 2an with n=1, then M is an Ocone local martingale with respect to its...

The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk increments, leads to some natural dynamics. In this paper we...

Importance sampling (IS) is a variance reduction method for simulating rare events. A recent paper by Dupuis, Wang and Sezer [Paul Dupuis, Ali Devin Sezer, Hui Wang, Dynamic importance sampling for queueing networks, Annals of Applied Probability 17 (4) (2007) 1306-1346] exploits connections...

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and Gaussian distributions for various functionals of the process.

This paper investigates the relationship between the minimal Hellinger martingale measure of order q (MHM measure hereafter) and the q-optimal martingale measure for any q[not equal to]1. First, we provide more results for the MHM measure; in particular we establish its complete characterization...

We study the scaling limit for the height one field of the two-dimensional Abelian sandpile model. The scaling limit for the covariance having height one at two macroscopically distant sites, more generally the centred height one joint moment of a finite number of macroscopically distant sites,...