Gapeev, Pavel V. and Shiryaev, Albert N. (2011) On the sequential testing problem for some diffusion processes. Stochastics: an international journal of probability and stochastic processes, 83 (4-6). pp. 519-535. ISSN 1744-2508
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.
|Additional Information:||© 2011 Taylor & Francis|
|Uncontrolled Keywords:||sequential testing, diffusion process, two-dimensional optimal stopping, stochastic boundary, parabolic-type free-boundary problem, a change-of-variable formula with local time on surfaces|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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