Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions
Baudoin, Fabrice ; Ouyang, Cheng ; Tindel, Samy
Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014), p. 111-135 / Harvested from Numdam
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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.

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.

@article{AIHPB_2014__50_1_111_0,
     author = {Baudoin, Fabrice and Ouyang, Cheng and Tindel, Samy},
     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},
     volume = {50},
     year = {2014},
     pages = {111-135},
     doi = {10.1214/12-AIHP522},
     mrnumber = {3161525},
     zbl = {1286.60051},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2014__50_1_111_0}
}

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, Tome 50 (2014) pp. 111-135. doi : 10.1214/12-AIHP522. http://gdmltest.u-ga.fr/item/AIHPB_2014__50_1_111_0/

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