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Sequential testing of a Wiener process with costly observations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
(English)Article in journal (Other academic) Submitted
Abstract [en]

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.

National Category
Probability Theory and Statistics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-316571OAI: oai:DiVA.org:uu-316571DiVA: diva2:1078320
Available from: 2017-03-03 Created: 2017-03-03 Last updated: 2017-03-22
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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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