On states of exit measures for superdiffusions

Abstract

We consider the exit measures of $(L,\alpha)$-superdiffusions, $1 < \alpha \leq 2$, from a bounded smooth domain D in R ^d. By using analytic results about solutions of the corresponding boundary value problem, we study the states of the exit measures. (Abraham and Le Gall investigated earlier .this problem for a special case $L = \Delta$ and $\alpha = 2$). Also as an application of these analytic results, we give a different proof for the critical Hausdorff. dimension of boundary polarity (established earlier by Le Gall under more restrictive assumptions and by Dynkin and Kuznetsov for general situations).