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

M. Besalú; A. Kohatsu-Higa; S. Tindel

doi:10.1214/14-aop977

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arXiv · 1310.5798

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

M. Besalú·A. Kohatsu-Higa·S. Tindel

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Abstract

In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise, our study encompasses all parameters $H\in(0,1)$, while the multidimensional case is restricted to the case $H>1/2$. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.

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M. Besalú, A. Kohatsu-Higa, S. Tindel. 2016-02-11. Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions. https://doi.org/10.1214/14-aop977

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