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Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion
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Hairer, Martin and Pillai, N. S. (2011) Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol.47 (No.2). pp. 601-628. doi:10.1214/10-AIHP377 ISSN 0246-0203.
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Official URL: http://dx.doi.org/10.1214/10-AIHP377
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 enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition 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: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 0246-0203 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.47 | ||||
Number: | No.2 | ||||
Page Range: | pp. 601-628 | ||||
DOI: | 10.1214/10-AIHP377 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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