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arXiv · 1904.07227

First passage time for Slepian process with linear barrier

Jack Noonan·Anatoly Zhigljavsky
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Abstract

In this paper we extend results of L.A. Shepp by finding explicit formulas for the first passage probability $F_{a,b}(T\, |\, x)={\rm Pr}(S(t) 0$, where $S(t)$ is a Gaussian process with mean 0 and covariance $\mathbb{E} S(t)S(t')=\max\{0,1-|t-t'|\}\,.$ We then extend the results to the case of piecewise-linear barriers and outline applications to change-point detection problems. Previously, explicit formulas for $F_{a,b}(T\, |\, x)$ were known only for the cases $b=0$ (constant barrier) or $T\leq 1$ (short interval).

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BibTeXRIS

Jack Noonan, Anatoly Zhigljavsky. 2019-04-14. First passage time for Slepian process with linear barrier. https://arxiv.org/abs/1904.07227

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