A function $f(t)$ such that $f(t) / \sqrt{t+1} \uparrow a$ is considered. We define $T = \inf \{t: |W(t)| = f(t)\}$, where $W(t)$ is the Wiener process starting from 0. A sufficient condition for $E\{T^\mu\}$ to be finite is given.
Publié le : 1982-11-14
Classification:
Wiener process,
square root boundary,
exit times,
60J65
@article{1176993723,
author = {Taksar, M. I.},
title = {First Hitting Time of Curvilinear Boundary by Wiener Process},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 1029-1031},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993723}
}
Taksar, M. I. First Hitting Time of Curvilinear Boundary by Wiener Process. Ann. Probab., Tome 10 (1982) no. 4, pp. 1029-1031. http://gdmltest.u-ga.fr/item/1176993723/