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SURE shrinkage of gaussian paths and signal identification

Nicolas Privault, Anthony Réveillac (2011)

ESAIM: Probability and Statistics

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.

SURE shrinkage of Gaussian paths and signal identification*

Nicolas Privault, Anthony Réveillac (2012)

ESAIM: Probability and Statistics

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.

Survival of homogeneous fragmentation processes with killing

Robert Knobloch, Andreas E. Kyprianou (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider a homogeneous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the decay of the largest fragment for parameter values that allow for survival. In this respect the present paper is also concerned with the probability of extinction of the killed process.

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