Asymptotically pointwise optimal and asymptotically optimal stopping times in the Bayesian inference

The paper deals with the problem of determining asymptotically pointwise optimal and asymptotically optimal stopping times in the Bayesian inference. The sufficient conditions are given for a family of stopping times to be asymptotically pointwise optimal and asymptotically optimal with respect to a continuous time process. As an example a sequential estimation of the intensity of the Poisson process is considered. Under a gamma prior distribution, an asymptotically pointwise optimal and asymptotically optimal rule is given using a LINEX loss function and the cost c per unit time.