scholarly journals Optimal and Asymptotically Optimal CUSUM Rules for Change Point Detection in the Brownian Motion Model with Multiple Alternatives

2006 ◽  
Vol 50 (1) ◽  
pp. 75-85 ◽  
Author(s):  
O. Hadjiliadis ◽  
V. Moustakides
Keyword(s):  
Brownian Motion ◽  
Change Point ◽  
Change Point Detection ◽  
Motion Model ◽  
Asymptotically Optimal ◽  
Brownian Motion Model ◽  
Point Detection

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

Extremes ◽  
2021 ◽  
Author(s):  
Anatoly Zhigljavsky ◽  
Jack Noonan
Keyword(s):  
Brownian Motion ◽  
Wiener Process ◽  
Change Point ◽  
Piecewise Linear ◽  
Change Point Detection ◽  
First Passage Times ◽  
First Passage ◽  
Explicit Formulas ◽  
Point Detection ◽  
Passage Times

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.

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