We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are...

Lanchier and Neuhauser have initiated the study of host-symbiont systems but have concentrated on the case in which the birth rates for unassociated hosts are equal. Here we allow the birth rates to be different and identify cases in which a host with a specialist pathogen can coexist with a...

We study the probability distribution F(u) of the maximum of smooth Gaussian fields defined on compact subsets of having some geometric regularity. Our main result is a general expression for the density of F. Even though this is an implicit formula, one can deduce from it explicit bounds for...

For a class of Gaussian stationary processes, the spectral density f[theta]([lambda]),[theta]=([tau]',[eta]')', is assumed to be a piecewise continuous function, where [tau] describes the discontinuity points, and the piecewise spectral forms are smoothly parameterized by [eta]. Although...

This paper is devoted to real valued backward stochastic differential equations (BSDEs for short) with generators which satisfy a stochastic Lipschitz condition involving BMO martingales. This framework arises naturally when looking at the BSDE satisfied by the gradient of the solution to a BSDE...

A continuous time random walk (CTRW) is a random walk subordinated to a renewal process, used in physics to model anomalous diffusion. Transition densities of CTRW scaling limits solve fractional diffusion equations. This paper develops more general limit theorems, based on triangular arrays,...

We study the problem of density estimation of a non-degenerate diffusion using kernel functions. Thanks to Malliavin calculus techniques, we obtain an expansion of the discretization error. Then, we introduce a new control variate method in order to reduce the variance in the density estimation....

By means of a multi-scale analysis we describe the typical geometrical structure of the clusters under the FK measure in random media. Our result holds in any dimension d[greater-or-equal, slanted]2 provided that slab percolation occurs under the averaged measure, which should be the case for...

The problem of sequence comparison via optimal alignments occurs naturally in many areas of applications. The simplest such technique is based on evaluating a score given by the length of a longest common subsequence divided by the average length of the original sequences. In this paper we...

The aim of this paper is to establish a change of variable formula for general Gaussian processes whose covariance function satisfies some technical conditions. The stochastic integral is defined in the Stratonovich sense using an approximation by middle point Riemann sums. The change of...