We derive quenched subdiffusive lower bounds for the exit time τ(n) from a box of size n for the simple random walk on the planar invasion percolation cluster. The first part of the paper is devoted to proving an almost sure analogue of H. Kesten’s subdiffusivity theorem for the random walk...

We study a class of self-similar jump type SDEs driven by Hölder continuous drift and noise coefficients. Using the Lamperti transformation for positive self-similar Markov processes we obtain a necessary and sufficient condition for almost sure extinction in finite time. We then show that in...