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

Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 and Noonan, Jack 2021. First passage times for Slepian process with linear and piecewise linear barriers. Extremes 24 , pp. 565-589. 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:	Publication
Status:	Published
Schools:	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:	05 May 2023 12:05
URI:	https://orca.cardiff.ac.uk/id/eprint/138524

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