Sequential testing problems for some diffusion processes
- Gapeev, Pavel
2010 Mathematics Subject Classification
- 60G40 62M20 34K10 62C10 62L15 60J60
- Sequential testing, diffusion process, optimal stopping, free-boundary problem, smooth-fit condition, Itô's formula
We study the Bayesian problem of sequential testing of two simple hypotheses about the local drift of an observed diffusion process. The optimal stopping time is found as the first time when the a posteriori probability process leaves the region defined by two stochastic boundaries depending on the observation process. It is shown that under some nontrivial relationships on the coefficients of the observed diffusion the problem admits a closed form solution. The method of proof is based on embedding the initial problem into a two-dimensional optimal stopping problem and solving the equivalent free-boundary problem by means of the smooth-fit conditions.