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).
Primary Subjects: 60J60, 35J65
Secondary Subjects: 60J80, 60J25, 31C45, 35J60
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HSINCHU, TAIWAN E-mail: sheu@math.nctu.edu.tw
