Hairer, Martin and Pillai, Natesh S., 1981- (2009) Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

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Abstract

We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H > 1/2 have similar ergodic properties as SDEs driven by standard Brownian motion. The focus in this article is on hypoelliptic systems satisfying Hormander’s condition. We show that such systems satisfy a suitable version of the strong Feller property and we conclude that they admit a unique stationary solution that is physical in the sense that it does not "look into the future". The main technical result required for the analysis is a bound on the moments of the inverse of the Malliavin covariance matrix, conditional on the past of the driving noise.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Stochastic differential equations, Brownian motion processes, Ergodic theory
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2009
Volume:	Vol.2009
Number:	No.38
Number of Pages:	28
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/35225

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