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April, 1976 Boundary Crossing Probabilities for Sample Sums and Confidence Sequences
Tze Leung Lai
Ann. Probab. 4(2): 299-312 (April, 1976). DOI: 10.1214/aop/1176996135


By making use of the martingale $\int^\infty_0 \exp (yW(t) - (t/2)y^2) dF(y)$, Robbins and Siegmund have evaluated the probability that the Wiener process $W(t)$ would ever cross certain moving boundaries. In this paper, we study this class of boundaries and make use of certain moment generating function martingales to obtain boundary crossing probabilities for sums of i.i.d. random variables. Invariance theorems for these boundary crossing probabilities are proved, and some applications to confidence sequences and power-one tests are also given.


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Tze Leung Lai. "Boundary Crossing Probabilities for Sample Sums and Confidence Sequences." Ann. Probab. 4 (2) 299 - 312, April, 1976.


Published: April, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0344.60024
MathSciNet: MR405578
Digital Object Identifier: 10.1214/aop/1176996135

Primary: 60F99
Secondary: 62L10

Keywords: boundary crossing probabilities , Confidence sequences , moment generating function martingales , Robbins-Siegmund boundaries , sample sums , Wiener process

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 2 • April, 1976
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