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Teor. Veroyatnost. i Primenen., 2012, Volume 57, Issue 4, Pages 778–788 (Mi tvp4480)  

This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

On Chernoffs hypotheses testing problem for the drift of a Brownian motion

M. V. Zhitlukhin, A. A. Muravlev

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: This paper contains detailed exposition of the results presented in the short communication [M. V. Zhitlukhin and A. A. Muravlev, Russian Math. Surveys, 66 (2011), pp. 10121013]. We consider Chernoffs problem of sequential testing of two hypotheses about the sign of the drift of a Brownian motion under the assumption that it is normally distributed. We obtain an integral equation which characterizes the optimal decision rule and find its solution numerically.

Keywords: Chernoffs problem; sequential hypotheses testing; optimal stopping problem; integral equations.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0073
14.740.11.1144
Russian Foundation for Basic Research 12-01-31449-


DOI: https://doi.org/10.4213/tvp4480

Full text: PDF file (202 kB)
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English version:
Theory of Probability and its Applications, 2013, 57:4, 708–717

Bibliographic databases:

Document Type: Article
MSC: 60
Received: 07.08.2012

Citation: M. V. Zhitlukhin, A. A. Muravlev, “On Chernoffs hypotheses testing problem for the drift of a Brownian motion”, Teor. Veroyatnost. i Primenen., 57:4 (2012), 778–788; Theory Probab. Appl., 57:4 (2013), 708–717

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Muravlev, “Methods of sequential hypothesis testing for the drift of a fractional Brownian motion”, Russian Math. Surveys, 68:3 (2013), 577–579  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. M. V. Zhitlukhin, A. N. Shiryaev, “On the existence of solutions of unbounded optimal stopping problems”, Proc. Steklov Inst. Math., 287:1 (2014), 299–307  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Ekstrom E., Vaicenavicius J., “Bayesian Sequential Testing of the Drift of a Brownian Motion”, ESAIM-Prob. Stat., 19 (2015), 626–648  crossref  mathscinet  zmath  isi
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