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, Volume 50 (2014) no. 1, pp. 111-135.

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.

Dans ce papier nous étudions des bornes supérieures pour la densité d’une solution déquation différentielle conduite par un mouvement brownien fractionnaire d’indice de Hurst H>1/3. Nous montrons, que sous certaines conditions géomètriques, dans le cas régulier H>1/2, la densité de la solution satisfait l’inégalité de log-Sobolev, l’inégalité de concentration gaussienne et admet une borne supérieure gaullienne. Dans le cas H>1/3 et sous la même condition géomètrique, nous montrons que la densité est infiniment différentiable et admet une borne supérieure sous-gaussienne.

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     title = {Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {111--135},
     publisher = {Gauthier-Villars},
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     url = {http://archive.numdam.org/articles/10.1214/12-AIHP522/}
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Baudoin, Fabrice; Ouyang, Cheng; 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, Volume 50 (2014) no. 1, pp. 111-135. doi : 10.1214/12-AIHP522. http://archive.numdam.org/articles/10.1214/12-AIHP522/

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