Smoothing and occupation measures of stochastic processes

Mario Wschebor[1]

  • [1] Centro de Matemática, Facultad de Ciencias, Universidad de la República, Calle Iguá 4225. 11400, Montevideo (Uruguay).

Annales de la faculté des sciences de Toulouse Mathématiques (2006)

  • Volume: 15, Issue: 1, page 125-156
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Wschebor, Mario. "Smoothing and occupation measures of stochastic processes." Annales de la faculté des sciences de Toulouse Mathématiques 15.1 (2006): 125-156. <http://eudml.org/doc/10029>.

@article{Wschebor2006,
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.},
affiliation = {Centro de Matemática, Facultad de Ciencias, Universidad de la República, Calle Iguá 4225. 11400, Montevideo (Uruguay).},
author = {Wschebor, Mario},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
number = {1},
pages = {125-156},
publisher = {Université Paul Sabatier, Toulouse},
title = {Smoothing and occupation measures of stochastic processes},
url = {http://eudml.org/doc/10029},
volume = {15},
year = {2006},
}

TY - JOUR
AU - Wschebor, Mario
TI - Smoothing and occupation measures of stochastic processes
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2006
PB - Université Paul Sabatier, Toulouse
VL - 15
IS - 1
SP - 125
EP - 156
AB - 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.
LA - eng
UR - http://eudml.org/doc/10029
ER -

References

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