On Estimation of the Mean in a Multivariate Normal Population with Discontinuous a priori Density

The article investigates the behavior of the risk of the Bayesian estimate of a signal $\Theta$ in additive Gaussian noise up to turns of second-order smallness inclusive. It is assumed that the a priori density of the parameter is 0 outside of some compactum and is discontinuous on the boundary of this compactum.