# 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

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topBaudoin, 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 $H>1/3$. We show that under some geometric conditions, in the regular case $H>1/2$, the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case $H>1/3$ 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 $H>1/3$. We show that under some geometric conditions, in the regular case $H>1/2$, the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case $H>1/3$ 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 -

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