A Malliavin calculus method to study densities of additive functionals of SDE’s with irregular drifts

Arturo Kohatsu-Higa; Akihiro Tanaka

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 3, page 871-883
  • ISSN: 0246-0203

Abstract

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We present a general method which allows to use Malliavin Calculus for additive functionals of stochastic equations with irregular drift. This method uses the Girsanov theorem combined with Itô–Taylor expansion in order to obtain regularity properties for this density. We apply the methodology to the case of the Lebesgue integral of a diffusion with bounded and measurable drift.

How to cite

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Kohatsu-Higa, Arturo, and Tanaka, Akihiro. "A Malliavin calculus method to study densities of additive functionals of SDE’s with irregular drifts." Annales de l'I.H.P. Probabilités et statistiques 48.3 (2012): 871-883. <http://eudml.org/doc/272091>.

@article{Kohatsu2012,
abstract = {We present a general method which allows to use Malliavin Calculus for additive functionals of stochastic equations with irregular drift. This method uses the Girsanov theorem combined with Itô–Taylor expansion in order to obtain regularity properties for this density. We apply the methodology to the case of the Lebesgue integral of a diffusion with bounded and measurable drift.},
author = {Kohatsu-Higa, Arturo, Tanaka, Akihiro},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Malliavin calculus; non-smooth drift; density function},
language = {eng},
number = {3},
pages = {871-883},
publisher = {Gauthier-Villars},
title = {A Malliavin calculus method to study densities of additive functionals of SDE’s with irregular drifts},
url = {http://eudml.org/doc/272091},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Kohatsu-Higa, Arturo
AU - Tanaka, Akihiro
TI - A Malliavin calculus method to study densities of additive functionals of SDE’s with irregular drifts
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 3
SP - 871
EP - 883
AB - We present a general method which allows to use Malliavin Calculus for additive functionals of stochastic equations with irregular drift. This method uses the Girsanov theorem combined with Itô–Taylor expansion in order to obtain regularity properties for this density. We apply the methodology to the case of the Lebesgue integral of a diffusion with bounded and measurable drift.
LA - eng
KW - Malliavin calculus; non-smooth drift; density function
UR - http://eudml.org/doc/272091
ER -

References

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