The Annals of Probability

On states of exit measures for superdiffusions

Yuan-Chung Sheu

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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).

Article information

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

Dates
First available in Project Euclid: 15 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1042644716

Digital Object Identifier
doi:10.1214/aop/1042644716

Mathematical Reviews number (MathSciNet)
MR1387635

Zentralblatt MATH identifier
0854.60079

Subjects
Primary: 60J60: Diffusion processes [See also 58J65] 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J25: Continuous-time Markov processes on general state spaces 31C45: Other generalizations (nonlinear potential theory, etc.) 35J60: Nonlinear elliptic equations

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

Citation

Sheu, Yuan-Chung. On states of exit measures for superdiffusions. Ann. Probab. 24 (1996), no. 1, 268--279. doi:10.1214/aop/1042644716. https://projecteuclid.org/euclid.aop/1042644716


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