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 Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 4, Pages 713–729 (Mi tvp5183)

Sequential testing of two hypotheses for a stationary Ornstein–Uhlenbeck process

D. I. Lisovskii, A. N. Shiryaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The present paper is concerned with the conditionally extremal settings of the sequential testing problem of two simple hypotheses about a parameter responsible for the local return rate of a stationary Ornstein–Uhlenbeck process to its mean value. Minimization of the Kullback–Leibler divergence is considered as an optimality test. An asymptotically optimal scheme is put forward, first, in the case when the error probabilities of the first and the second kind tend to zero, and, second, in the case when the tested parameters go off to infinity but the distance between them is fixed.

Keywords: sequential analysis, hypothesis testing, variational statement, fixed error probability formulation, conditionally extremal settings, SPRT, stationary Ornstein–Uhlenbeck process.

 Funding Agency Grant Number Russian Science Foundation 14-21-00162 This work was supported by the Russian Science Foundation (grant 14-21-00162).

DOI: https://doi.org/10.4213/tvp5183

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English version:
Theory of Probability and its Applications, 2019, 63:4, 580–593

Bibliographic databases:

Revised: 25.05.2018
Accepted:21.06.2018

Citation: D. I. Lisovskii, A. N. Shiryaev, “Sequential testing of two hypotheses for a stationary Ornstein–Uhlenbeck process”, Teor. Veroyatnost. i Primenen., 63:4 (2018), 713–729; Theory Probab. Appl., 63:4 (2019), 580–593

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tvp5183
• https://doi.org/10.4213/tvp5183
• http://mi.mathnet.ru/eng/tvp/v63/i4/p713

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This publication is cited in the following articles:
1. “Abstracts of talks given at the 3rd International Conference on Stochastic Methods”, Theory Probab. Appl., 64:1 (2019), 124–169
2. S. Ankirchner, M. Klein, “Bayesian sequential testing with expectation constraints”, ESAIM-Control OPtim. Calc. Var., 26 (2020), 51
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