Let $\{X_t, t \geqq 0\}$ be a process with stationary independent increments taking values in $d$-dimensional Euclidean space. Let $S$ be a set in $R^d$, and let $T = \inf\{t > 0: X_t \not\in S\}$. For a reasonably wide class of processes and sets $S$, criteria are given for deciding when $P\{X_T \in B\} > 0$ and when $P\{X_T \in B\} = 0$, where $B \subset \partial S$.
Publié le : 1975-04-14
Classification:
Stochastic processes,
Markov process,
stationary independent increments,
Levy measure,
first passage distribution,
local growth,
sample function behavior,
60J30,
60G17,
60G10,
60G40,
60J25,
60J40
@article{1176996394,
author = {Millar, P. W.},
title = {First Passage Distributions of Processes With Independent Increments},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 215-233},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996394}
}
Millar, P. W. First Passage Distributions of Processes With Independent Increments. Ann. Probab., Tome 3 (1975) no. 6, pp. 215-233. http://gdmltest.u-ga.fr/item/1176996394/