Boundary crossing probabilities for stationary Gaussian processes and Brownian motion

Author:
Jack Cuzick

Journal:
Trans. Amer. Math. Soc. **263** (1981), 469-492

MSC:
Primary 60G15; Secondary 60F10, 60J65

DOI:
https://doi.org/10.1090/S0002-9947-1981-0594420-5

MathSciNet review:
594420

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a stationary Gaussian process, a continuous function, and a finite or infinite interval. This paper develops asymptotic estimates for , some when this probability is small. After transformation to an Ornstein Uhlenbeck process the results are also applicable to Brownian motion. In that special case, if is Brownian motion, is continuously differentiable, and our estimate for , some is

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0594420-5

Keywords:
Boundary crossing,
first passage time,
Gaussian process,
Brownian motion,
sequential analysis,
maxima

Article copyright:
© Copyright 1981
American Mathematical Society