Mathematics – Probability
Scientific paper
2008-06-24
Stochastic Processes and their Applications 119 (2009), pp. 924-936
Mathematics
Probability
16 pages; accepted for publication in "Stochastic Processes and their Applications"
Scientific paper
10.1016/j.spa.2008.06.002
In this note we present some examples of diffusions in random environment whose asymptotic behavior is rather surprising. We construct a family of diffusions that are small perturbations of Brownian motion with non-vanishing expected local drift under the static measure of the environment but where the ballistic behavior is lost. As slight modifications of this collection of diffusions we also provide examples with ballistic behavior where the non-vanishing limiting velocity points to a direction opposite to the expected local drift under the static measure.
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