Sequential testing of a Wiener process with costly observations. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Dyrssen, Hannah; Ekström, Erik
• Is Part Of: Sequential analysis. Volume 37:Issue 1(2018)
• Page Start: 47
• Page End: 58
• Publication Date: 2018-01-02
• Subjects: Brownian motion -- hypothesis testing -- optimal stopping -- sequential analysis; 62L10 -- 60G40 -- 62C10 -- 62L05; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2018.1427973
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: We consider the sequential testing of two simple hypotheses for the drift of a Brownian motion when each observation of the underlying process is associated with a positive cost. In this setting where continuous monitoring of the underlying process is not feasible, the question is not only whether to stop or to continue at a given observation time but also, if continuing, how to distribute the next observation time. Adopting a Bayesian methodology, we show that the value function can be characterized as the unique fixed point of an associated operator and that it can be constructed using an iterative scheme. Moreover, the optimal sequential distribution of observation times can be described in terms of the fixed point.