Location of Repository

CRiSM Paper No. 09-38, www.warwick.ac.uk/go/crism Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion

By M. Hairer and N. S. Pillai

Abstract

We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H> 1 have similar ergodic properties as 2 SDEs driven by standard Brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’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

Topics: Ergodicity, Fractional Brownian motion, Hörmander’s theorem
Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.412.5454
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www2.warwick.ac.uk/fac/... (external link)
  • www.warwick.ac.uk/go/crism (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.