J. Noonan

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19982022

most citedFirst passage time for Slepian process with linear barrier

1 citations · 1 across the 5 of their papers we have counts for

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math.PR2019★ 1 cited

First passage time for Slepian process with linear barrier

Jack Noonan, Anatoly Zhigljavsky

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)<a+bt \text{ for all } t\in[0,T]\,\, |…

math.PR2018

Approximating Shepp's constants for the Slepian process

Jack Noonan, Anatoly Zhigljavsky

Slepian process $S (t)$ is a stationary Gaussian process with zero mean and covariance $E S (t) S (t^{'}) = max {0, 1 - ∣ t - t^{'} ∣} .$ For any $T > 0$ and $h > 0$ , define $F_T(h ) = {\rm Pr}\lef…