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 Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 4, Pages 683–712 (Mi tvp5169)

Bayesian sequential testing problem for a Brownian bridge

D. I. Lisovskii

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The present paper gives a solution to the Bayesian sequential testing problem of two simple hypotheses about the mean of a Brownian bridge. The method of the proof is based on reducing the sequential analysis problem to the optimal stopping problem for a strong Markov posterior probability process. The key idea in solving the above problem is the application of the one-to-one Kolmogorov time-space transformation, which enables one to consider, instead of the optimal stopping problem on a finite time horizon for a time-inhomogeneous diffusion process, an optimal stopping problem on an infinite time horizon for a homogeneous diffusion process with a slightly more complicated risk functional. The continuation and stopping sets are determined by two continuous boundaries, which constitute a unique solution of a system of two nonlinear integral equations.

Keywords: sequential analysis, hypothesis testing problem, optimal stopping problem, Brownian bridge, Kolmogorov time-space transformation.

 Funding Agency Grant Number Russian Science Foundation 14-21-00162

DOI: https://doi.org/10.4213/tvp5169

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English version:
Theory of Probability and its Applications, 2019, 63:4, 556–579

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Revised: 29.06.2018

Citation: D. I. Lisovskii, “Bayesian sequential testing problem for a Brownian bridge”, Teor. Veroyatnost. i Primenen., 63:4 (2018), 683–712; Theory Probab. Appl., 63:4 (2019), 556–579

Citation in format AMSBIB
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