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March 2015 On the disorder problem for a negative binomial process
Bruno Buonaguidi, Pietro Muliere
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J. Appl. Probab. 52(1): 167-179 (March 2015). DOI: 10.1239/jap/1429282613

Abstract

We study the Bayesian disorder problem for a negative binomial process. The aim is to determine a stopping time which is as close as possible to the random and unknown moment at which a sequentially observed negative binomial process changes the value of its characterizing parameter p ∈ (0, 1). The solution to this problem is explicitly derived through the reduction of the original optimal stopping problem to an integro-differential free-boundary problem. A careful analysis of the free-boundary equation and of the probabilistic nature of the boundary point allows us to specify when the smooth fit principle holds and when it breaks down in favour of the continuous fit principle.

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Bruno Buonaguidi. Pietro Muliere. "On the disorder problem for a negative binomial process." J. Appl. Probab. 52 (1) 167 - 179, March 2015. https://doi.org/10.1239/jap/1429282613

Information

Published: March 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1328.60102
MathSciNet: MR3336853
Digital Object Identifier: 10.1239/jap/1429282613

Subjects:
Primary: 60G40
Secondary: 35R35 , 62C10 , 62L10

Keywords: disorder problem , free-boundary problem , negative binomial process , Optimal stopping , principles of continuous and smooth fit , regular boundary , sequential detection

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 1 • March 2015
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