Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior

The Bayesian estimator of the mean of the Poisson distribution under the gamma prior ([alpha]0, [beta]0) is stable (robust) in the sense that if the prior runs over the set {([alpha], [beta]0): [alpha][epsilon][[alpha]0-[delta], [alpha]0+[delta]]}, then the oscillat estimator with the oscillation O([delta]2) is constructed; it also minimizes the oscillation of the posterior risk when the shape parameter runs over a finite interval.