## The Annals of Probability

### First Passage Distributions of Processes With Independent Increments

P. W. Millar

#### Abstract

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 $B \subset \partial S$.

#### Article information

Source
Ann. Probab. Volume 3, Number 2 (1975), 215-233.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996394

Digital Object Identifier
doi:10.1214/aop/1176996394

Mathematical Reviews number (MathSciNet)
MR368177

Zentralblatt MATH identifier
0318.60063

JSTOR