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Evaluation of the first-passage time probability to a square root boundary for the Wiener process

Published online by Cambridge University Press:  14 July 2016

Shunsuke Sato
Affiliation:
Osaka University

Abstract

This paper gives an asymptotic evaluation of the probability that the Wiener path first crosses a square root boundary. The result is applied to estimate the moments of the first-passage time distribution of the Ornstein–Uhlenbeck process to a constant boundary.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1977 

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References

Breimann, L. (1966) First exit times from a square root boundary. Proc. 5th Berkeley Symp. Math. Statist. Prob. 2 (2), 916.Google Scholar
Capocelli, R. M. and Ricciardi, L. M. (1971) Diffusion approximation and first passage time problem for a model neuron. Kybernetik 8 (6), 214223.CrossRefGoogle ScholarPubMed
Durbin, J. (1971) Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov–Smirnov test. J. Appl. Prob. 8, 431453.CrossRefGoogle Scholar
Shepp, L. A. (1967) A first passage problem for the Wiener process. Ann. Math. Statist. 38, 19121914.CrossRefGoogle Scholar
Siegert, A. J. F. (1951) On the first-passage-time probability function. Phys. Rev. 81, 617623.CrossRefGoogle Scholar
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