First passage times for Slepian process with linear and piecewise linear barriers

Zhigljavsky, Anatoly and Noonan, Jack 2021. First passage times for Slepian process with linear and piecewise linear barriers. Extremes 10.1007/s10687-021-00406-6

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Abstract

In this paper, we derive explicit formulas for the first-passage probabilities of the process S(t) = W(t) − W(t + 1), where W(t) is the Brownian motion, for linear and piece-wise linear barriers on arbitrary intervals [0,T]. Previously, explicit formulas for the first-passage probabilities of this process were known only for the cases of a constant barrier or T ≤ 1. The first-passage probabilities results are used to derive explicit formulas for the power of a familiar test for change-point detection in the Wiener process.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Mathematics
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher:	Springer Verlag
ISSN:	1386-1999
Date of First Compliant Deposit:	16 February 2021
Date of Acceptance:	7 January 2021
Last Modified:	16 Feb 2021 10:45
URI:	http://orca.cf.ac.uk/id/eprint/138524

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