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Mario Wschebor
Smoothing and occupation measures of stochastic processes
Annales de la faculté des sciences de Toulouse Sér. 6, 15 no. 1 (2006), p. 125-156, doi: 10.5802/afst.1116
Article PDF | Reviews MR 2225750 | Zbl 1121.62072

Résumé - Abstract

This is a review paper about some problems of statistical inference for one-parameter stochastic processes, mainly based upon the observation of a convolution of the path with a non-random kernel. Most of the results are known and presented without proofs. The tools are first and second order approximation theorems of the occupation measure of the path, by means of functionals defined on the smoothed paths. Various classes of stochastic processes are considered starting with the Wiener process, Gaussian processes, continuous semi-martingales and Lévy processes. Some statistical applications are also included in the text.

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