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2006 Examples of Condition $(T)$ for Diffusions in a Random Environment
Tom Schmitz
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Electron. J. Probab. 11: 540-562 (2006). DOI: 10.1214/EJP.v11-337


With the help of the methods developed in our previous article [Schmitz, to appear in Annales de l'I.H.P., in press], we highlight condition $(T)$ as a source of new examples of 'ballistic' diffusions in a random environment when $d>1$ ('ballistic' means that a strong law of large numbers with non-vanishing limiting velocity holds). In particular we are able to treat the case of non-constant diffusion coefficients, a feature that causes problems. Further we recover the ballistic character of two important classes of diffusions in a random environment by simply checking condition $(T)$. This not only points out to the broad range of examples where condition $(T)$ can be checked, but also fortifies our belief that condition $(T)$ is a natural contender for the characterisation of ballistic diffusions in a random environment when $d>1$.


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Tom Schmitz. "Examples of Condition $(T)$ for Diffusions in a Random Environment." Electron. J. Probab. 11 540 - 562, 2006.


Accepted: 1 August 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1109.60088
MathSciNet: MR2242655
Digital Object Identifier: 10.1214/EJP.v11-337

Primary: 60K37
Secondary: 82D30

Keywords: ballistic behavior , Condition $(T)$ , Diffusions in a random environment


Vol.11 • 2006
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