We prove the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H0.5. The result is based on the Fréchet differentiability with respect to the input function for deterministic differential equations driven by...

The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the...

In this paper, we investigate the properties of the recently introduced measure of dependence called correlation cascade. We show that the correlation cascade is a promising tool for studying the dependence structure of infinitely divisible processes. We describe the ergodic properties...

The preservation of the semi-martingale property in progressive enlargement of filtrations has been studied by many authors. Most of them focus on progressive enlargement with a honest time, allowing for semi-martingale invariance and simple decomposition formulas. However, times allowing for...

We give large deviation results for the super-Brownian excursion conditioned to have unit mass or unit extinction time and for super-Brownian motion with constant non-positive drift. We use a representation of these processes by a path-valued process, the so-called Brownian snake for which we...

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such...

The notion of a separating time for a pair of measures on a filtered space is helpful for studying problems of (local) absolute continuity and singularity of measures. In this paper, we describe a certain canonical setting for continuous local martingales (abbreviated below as CLMs) and find an...

The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change dramatically. We study this phenomenon in the context of functional...

Covariances play a fundamental role in the theory of stationary processes and they can naturally be estimated by sample covariances. There is a well-developed asymptotic theory for sample covariances of linear processes. For nonlinear processes, however, many important problems on their...

We obtain rates of strong approximation of the empirical process indexed by functions by a Brownian bridge under only random entropy conditions. The results of Berthet and Mason [P. Berthet, D.M. Mason, Revisiting two strong approximation results of Dudley and Philipp, in: High Dimensional...