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Type: Artigo de periódico
Title: Ergodic theory for sdes with extrinsic memory
Author: Hairer, M
Ohashi, A
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.
Subject: non-Markovian processes
fractional Brownian motion
Country: EUA
Editor: Inst Mathematical Statistics
Citation: Annals Of Probability. Inst Mathematical Statistics, v. 35, n. 5, n. 1950, n. 1977, 2007.
Rights: aberto
Identifier DOI: 10.1214/009117906000001141
Date Issue: 2007
Appears in Collections:Unicamp - Artigos e Outros Documentos

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