Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of gaussian fields. Among several examples, we provide an application to a functional version of the Breuer–Major CLT for fields subordinated to a fractional brownian motion.
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