On states of exit measures for superdiffusions

Abstract

We consider the exit measures of (L, alpha)-superdiffusions, 1 < alpha less than or equal to 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).