On the optimal stopping with incomplete data

The Kalman–Bucy continuous model of partially observable stochastic processes is considered. The problem of optimal stopping of a stochastic process with incomplete data is reduced to the problem of optimal stopping with complete data. The convergence of payoffs is proved when ${\epsilon }_1\to 0,{\epsilon }_2\to 0$, where ${\epsilon }_1,$ and ${\epsilon }_2$ are small perturbation parameters of the non observable and observable processes respectively.