The Annals of Probability

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

M. Besalú, A. Kohatsu-Higa, and 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.

Article information

Source
Ann. Probab., Volume 44, Number 1 (2016), 399-443.

Dates
Received: October 2013
Revised: September 2014
First available in Project Euclid: 2 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1454423045

Digital Object Identifier
doi:10.1214/14-AOP977

Mathematical Reviews number (MathSciNet)
MR3456342

Zentralblatt MATH identifier
1341.60049

Subjects
Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 34K50: Stochastic functional-differential equations [See also , 60Hxx] 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Fractional Brownian motion stochastic equations density function estimates

Citation

Besalú, M.; Kohatsu-Higa, A.; Tindel, S. Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions. Ann. Probab. 44 (2016), no. 1, 399--443. doi:10.1214/14-AOP977. https://projecteuclid.org/euclid.aop/1454423045


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