The distribution of Brownian motion on linear stopping boundaries. (English) Zbl 0884.62093
Sequential Anal. 16, No. 4, 345-352 (1997); addendum ibid. 17, No. 1, 123-124 (1998).
Summary: We consider Brownian motion with drift and stopping boundaries: linear upper and lower boundaries, and possibly a vertical boundary at a truncation point, all under conditions assuring a finite stopping time. T. W. Anderson [Ann. Math. Stat. 31, 165-197 (1960; Zbl 0089.35501)] derived formulas for the distributions of the stopped process along these boundaries and for the associated expected stopping times. We present simpler formulas, and briefer derivations.
MSC:
| 62M02 | Markov processes: hypothesis testing |
| 62L10 | Sequential statistical analysis |
| 62E15 | Exact distribution theory in statistics |
| 60J65 | Brownian motion |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
Keywords:
sequential tests; Brownian bridge; likelihood ratio identity; inverse Gaussian distributionCitations:
Zbl 0089.35501References:
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