The Annals of Probability

First Passage Distributions of Processes With Independent Increments

P. W. Millar

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60J30
Secondary: 60G17: Sample path properties 60G10: Stationary processes 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J25: Continuous-time Markov processes on general state spaces 60J40: Right processes

Keywords
Stochastic processes Markov process stationary independent increments Levy measure first passage distribution local growth sample function behavior

Citation

Millar, P. W. First Passage Distributions of Processes With Independent Increments. Ann. Probab. 3 (1975), no. 2, 215--233. doi:10.1214/aop/1176996394. https://projecteuclid.org/euclid.aop/1176996394


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