Gaussian type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions

Mireia Besalú (1, 2) , Arturo Kohatsu-Higa (3) , Samy Tindel (2, 1)

1 IECL - Institut Élie Cartan de Lorraine
2 BIGS - Biology, genetics and statistics
3 Department of Mathematical Sciences, Ritsumeikan Universtiy

In this paper we obtain Gaussian type lower bounds for the density of solutions to stochastic differential equations (sde's) driven by a fractional Brownian motion with Hurst parameter H. In the one dimensional case with additive noise, our study encompasses all parameters 01/2. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.

Mots clés: density function estimate; stochastic equations; Fractional Brownian motion

Domaines: Probabilités [math.PR]

Mireia Besalú, Arturo Kohatsu-Higa, Samy Tindel. Gaussian type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions. [Research Report] non spécifié. 2013. ⟨hal-00875378⟩