Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion
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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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|
|Number of Pages:||28|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
[Arn98] L. ARNOLD. Random dynamical systems. Springer Monographs in Mathematics.
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