Degenerate limit laws for the maxima of trigonometric polynomials with random coefficients
Delay equations driven by rough paths.
Density formula and concentration inequalities with Malliavin calculus.
Des résultats nouveaux sur les processus gaussiens
Description de certains processus markoviens indexés par des sous-ensembles du cercle
Deux exemples d'utilisation de mesures majorantes
Die Anzahl der lokalen Maximalstellen eines stationären Gauszschen Prozesses.
Differential equations driven by gaussian signals
We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.
Distance de Fortet-Mourier et fonctions log-concaves
Distortion mismatch in the quantization of probability measures
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a probability distribution P on when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
Distributions gaussiennes et temps locaux d'intersection