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Linearization techniques for 𝕃 ∞ See PDF-control problems and dynamic programming principles in classical and 𝕃 ∞ See PDF-control problems

Dan Goreac;  Oana-Silvia Serea — 2012

ESAIM: Control, Optimisation and Calculus of Variations

The aim of the paper is to provide a linearization approach to the 𝕃 ∞ See PDF-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the 𝕃 p See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating 𝕃 ∞ See PDF problems in continuous and lower semicontinuous...

Linearization techniques for See PDF -control problems and dynamic programming principles in classical and See PDF -control problems

Dan Goreac;  Oana-Silvia Serea — 2012

ESAIM: Control, Optimisation and Calculus of Variations

The aim of the paper is to provide a linearization approach to the See PDF -control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating See PDF problems in continuous and lower semicontinuous setting.

A note on the adaptive estimation of the differential entropy by wavelet methods

Christophe Chesneau;  Fabien Navarro;  Oana Silvia Serea — 2017

Commentationes Mathematicae Universitatis Carolinae

In this note we consider the estimation of the differential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean 𝕃 p error, p ≥ 1 , this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical findings.

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