Fisher information and detection of a Euclidean perturbation of an independent stationary process (Q1075690)

Let \((X_ 1,X_ 2,...)\) be a stationary process of independent d- variate quantities. Let a process \((g_ 1X_ 1,g_ 2X_ 2,...)\) be generated by the original one by means of a sequence \((g_ 1,g_ 2,...)\) of Euclidean rigid motions (translations, rotations and their compositions). The author gives conditions under which these processes are singular or absolutely continuous. Necessary and sufficient conditions of absolute continuity are given in terms of finite Fisher information.