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Ergodic theory for SDEs with extrinsic memory
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Hairer, Martin and Ohashi, A. (2007) Ergodic theory for SDEs with extrinsic memory. Annals of Probability, Vol.35 (No.5). pp. 1950-1977. doi:10.1214/009117906000001141 ISSN 0091-1798.
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Official URL: http://dx.doi.org/10.1214/009117906000001141
Abstract
We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a class of non-Markovian systems. They allow us to obtain a criteria for ergodicity which is similar in nature to the Doob-Khas'minskii theorem.
The second part of this article shows how it is possible to apply these results to the case of stochastic differential equations driven by fractional Brownian motion. It follows that under a nondegeneracy condition on the noise, such equations admit a unique adapted stationary solution.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Annals of Probability | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 0091-1798 | ||||
Official Date: | September 2007 | ||||
Dates: |
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Volume: | Vol.35 | ||||
Number: | No.5 | ||||
Number of Pages: | 28 | ||||
Page Range: | pp. 1950-1977 | ||||
DOI: | 10.1214/009117906000001141 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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