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

DeBlassie, R. Dante

Ann. Probab., Tome 18 (1990) no. 4, p. 1034-1070 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1990-07-14
Classification:  Symmetric stable process,  exit time,  wedge,  60G99,  60J25