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Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion
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Hairer, Martin and Pillai, Natesh S. (2009) Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.38).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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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 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.2009 | ||||
Number: | No.38 | ||||
Number of Pages: | 28 | ||||
Institution: | University of Warwick | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
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