First passage times for Slepian process with linear and piecewise linear barriers
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AbstractIn 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.
2018 ◽
Vol 490
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pp. 439-450
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2012 ◽
Vol 136
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pp. 175103
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2016 ◽
Vol 48
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pp. 1045-1060
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2005 ◽
Vol 50
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pp. 131-144
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2016 ◽
Vol 296
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pp. 275-292
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