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 $B \subset \partial S$.
Citation
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
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