Bayesian sequential testing of the drift of a Brownian motion

@article{Ekstrom2015BayesianST,
  title={Bayesian sequential testing of the drift of a Brownian motion},
  author={Erik Ekstrom and Juozas Vaicenavicius},
  journal={arXiv: Probability},
  year={2015}
}
We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior distributions. The statistical problem is reformulated as an optimal stopping problem with the current conditional probability that the drift is non-negative as the underlying process. The volatility of this conditional probability process is shown to be non-increasing… 

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