Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions

Fabrice Baudoin; Cheng Ouyang; Samy Tindel

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 1, page 111-135
  • ISSN: 0246-0203

Abstract

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In this paper we study upper bounds for the density of solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H g t ; 1 / 3 . We show that under some geometric conditions, in the regular case H g t ; 1 / 2 , the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case H g t ; 1 / 3 and under the same geometric conditions, we show that the density of the solution is smooth and admits an upper sub-Gaussian bound.

How to cite

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Baudoin, Fabrice, Ouyang, Cheng, and Tindel, Samy. "Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions." Annales de l'I.H.P. Probabilités et statistiques 50.1 (2014): 111-135. <http://eudml.org/doc/272082>.

@article{Baudoin2014,
abstract = {In this paper we study upper bounds for the density of solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H&gt;1/3$. We show that under some geometric conditions, in the regular case $H&gt;1/2$, the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case $H&gt;1/3$ and under the same geometric conditions, we show that the density of the solution is smooth and admits an upper sub-Gaussian bound.},
author = {Baudoin, Fabrice, Ouyang, Cheng, Tindel, Samy},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {1},
pages = {111-135},
publisher = {Gauthier-Villars},
title = {Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions},
url = {http://eudml.org/doc/272082},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Baudoin, Fabrice
AU - Ouyang, Cheng
AU - Tindel, Samy
TI - Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 1
SP - 111
EP - 135
AB - In this paper we study upper bounds for the density of solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H&gt;1/3$. We show that under some geometric conditions, in the regular case $H&gt;1/2$, the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case $H&gt;1/3$ and under the same geometric conditions, we show that the density of the solution is smooth and admits an upper sub-Gaussian bound.
LA - eng
UR - http://eudml.org/doc/272082
ER -

References

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