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Fisher information and detection of a Euclidean perturbation of an independent stationary process. (English) Zbl 0592.60033
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.
Reviewer: L.I.Gal’chuk

60G30 Continuity and singularity of induced measures
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60G10 Stationary stochastic processes
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