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Ergodic properties of a class of non-Markovian processes
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Hairer, Martin (2009) Ergodic properties of a class of non-Markovian processes. In: Blath, Jochen and Mörters, Peter and Scheutzow, Michael, (eds.) Trends in stochastic analysis : festschrift in honour of Heinrich von Weizsäcker. London Mathematical Society lecture note series . Cambridge, U.K. ; New York: Cambridge University Press, pp. 65-98. ISBN 9780521718219
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Official URL: http://dx.doi.org/10.1017/CBO9781139107020.006
Abstract
We study a fairly general class of time-homogeneous stochastic evolutions driven by noises that are not white in time. As a consequence, the resulting processes do not have the Markov property. In this setting, we obtain constructive criteria for the uniqueness of stationary solutions that are very close in spirit to the existing criteria for Markov processes.
In the case of discrete time, where the driving noise consists of a stationary sequence of Gaussian random variables, we give optimal conditions on the spectral measure for our criteria to be applicable. In particular, we show that, under a certain assumption on the spectral density, our assumptions can be checked in virtually the same way as one would check that the Markov process obtained by replacing the driving sequence by a sequence of independent identically distributed Gaussian random variables is strong Feller and topologically irreducible. The results of the present paper are based on those obtained previously in the continuous time context of diffusions driven by fractional Brownian motion.
| Item Type: | Book Item | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Series Name: | London Mathematical Society lecture note series | ||||
| Publisher: | Cambridge University Press | ||||
| Place of Publication: | Cambridge, U.K. ; New York | ||||
| ISBN: | 9780521718219 | ||||
| Book Title: | Trends in stochastic analysis : festschrift in honour of Heinrich von Weizsäcker | ||||
| Editor: | Blath, Jochen and Mörters, Peter and Scheutzow, Michael | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Number of Pages: | 390 | ||||
| Page Range: | pp. 65-98 | ||||
| DOI: | 10.1017/CBO9781139107020.006 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
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