Limit velocity and zero--one laws for diffusions in random environment

Details Limit velocity and zero--one laws for diffusions in random environment Limit velocity and zero--one laws for diffusions in random environment

2005-12-02

arxiv.org/abs/math/0512061v2

Annals of Applied Probability 2006, Vol. 16, No. 3, 1086-1123

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000051 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000051

We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in this direction equals either zero or one. Combined with our results on the limiting velocity, this implies a strong law of large numbers in two dimensions.

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