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

Details Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions

2011-04-19

arxiv.org/abs/1104.3884v1

Mathematics

Probability

Scientific paper

In this paper we study upper bounds for the density of solution of 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 satisfy 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.

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