68 citations · 231 across the 47 of their papers we have counts for
4 papers · 1 filter
Stein estimation for the drift of Gaussian processes using the Malliavin calculus
Nicolas Privault, Anthony Réveillac
We consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of…
Stochastic analysis of Bernoulli processes
Nicolas Privault
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The top…
SURE shrinkage of Gaussian paths and signal identification
Nicolas Privault, Anthony Réveillac
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times. By almo…
Convex ordering for random vectors using predictable representation
Marc Arnaudon, Jean-Christophe Breton, Nicolas Privault
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our metho…