The Annals of Probability

The First Exit Time of a Two-Dimensional Symmetric Stable Process from a Wedge

R. Dante DeBlassie

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Abstract

Let $T_\theta$ be the first exit time of a symmetric stable process [with parameter $\alpha \in (0, 2)$] from a wedge of angle $2\theta, 0 < \theta < \pi$. Then there are constants $p_{\theta, \alpha} > 0$ such that for starting points $x$ in the wedge, $E_xT^p_\theta < \infty$ if $0 < p < p_{\theta, \alpha}$ and $E_xT^p_\theta = \infty$ if $p > p_{\theta, \alpha}$. We characterize $p_{\alpha, \theta}$ and obtain upper and lower bounds.

Article information

Source
Ann. Probab., Volume 18, Number 3 (1990), 1034-1070.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990735

Digital Object Identifier
doi:10.1214/aop/1176990735

Mathematical Reviews number (MathSciNet)
MR1062058

Zentralblatt MATH identifier
0709.60075

JSTOR
links.jstor.org

Subjects
Primary: 60G99: None of the above, but in this section
Secondary: 60J25: Continuous-time Markov processes on general state spaces

Keywords
Symmetric stable process exit time wedge

Citation

DeBlassie, R. Dante. The First Exit Time of a Two-Dimensional Symmetric Stable Process from a Wedge. Ann. Probab. 18 (1990), no. 3, 1034--1070. doi:10.1214/aop/1176990735. https://projecteuclid.org/euclid.aop/1176990735


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