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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 83, 2011 - Issue 4-6: Optimal stopping with Applications
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Original Articles

On the sequential testing problem for some diffusion processes

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Pages 519-535 | Received 30 Nov 2009, Accepted 05 Oct 2010, Published online: 10 Oct 2011
 

Abstract

We study the Bayesian problem of sequential testing of two simple hypotheses about the drift rate of an observable diffusion process. The optimal stopping time is found as the first time at which the posterior probability of one of the hypotheses exits a region restricted by two stochastic boundaries depending on the current observations. The proof is based on an embedding of the initial problem into a two-dimensional optimal stopping problem and the analysis of the associated parabolic-type free-boundary problem. We also show that the problem admits a closed-form solution under certain non-trivial relations between the coefficients of the observable diffusion.

2000 Mathematics Subject Classification::

Acknowledgements

The authors thank the Referee for his careful reading of the manuscript and useful comments. This research was partially supported by Deutsche Forschungsgemeinschaft through the SFB 649 Economic Risk.

Notes

Additional information

Notes on contributors

Albert N. Shiryaev

1 1. [email protected]

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