On states of exit measures for superdiffusions

On states of exit measures for superdiffusions

Yuan-Chung Sheu

Source: Ann. Probab. Volume 24, Number 1 (1996), 268-279.

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).

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Primary Subjects: 60J60, 35J65

Secondary Subjects: 60J80, 60J25, 31C45, 35J60

Keywords: Exit measure; superdiffusion; Hausdorff dimension; boundary polar set; absolutely continuous state; singular state

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1042644716
Mathematical Reviews number (MathSciNet): MR1387635
Digital Object Identifier: doi:10.1214/aop/1042644716
Zentralblatt MATH identifier: 0854.60079

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HSINCHU, TAIWAN E-mail: sheu@math.nctu.edu.tw

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