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January 2016 Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions
M. Besalú, A. Kohatsu-Higa, S. Tindel
Ann. Probab. 44(1): 399-443 (January 2016). DOI: 10.1214/14-AOP977

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. "Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions." Ann. Probab. 44 (1) 399 - 443, January 2016. https://doi.org/10.1214/14-AOP977

Information

Received: 1 October 2013; Revised: 1 September 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1341.60049
MathSciNet: MR3456342
Digital Object Identifier: 10.1214/14-AOP977

Subjects:
Primary: 60G22
Secondary: 34K50 , 60H07

Keywords: density function estimates , fractional Brownian motion , stochastic equations

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 1 • January 2016
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