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April, 1975 First Passage Distributions of Processes With Independent Increments
P. W. Millar
Ann. Probab. 3(2): 215-233 (April, 1975). DOI: 10.1214/aop/1176996394

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 $B \subset \partial S$.

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P. W. Millar. "First Passage Distributions of Processes With Independent Increments." Ann. Probab. 3 (2) 215 - 233, April, 1975. https://doi.org/10.1214/aop/1176996394

Information

Published: April, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0318.60063
MathSciNet: MR368177
Digital Object Identifier: 10.1214/aop/1176996394

Subjects:
Primary: 60J30
Secondary: 60G10 , 60G17 , 60G40 , 60J25 , 60J40

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

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • April, 1975
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