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We consider random walks where each path is equipped with a random weight which is stationary and independent in space and time. We show that under some assumptions the arising probability distributions are in a sense uniformly absolutely continuous with respect to the usual probability distribution for symmetric random walks.
We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.
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