Fisher information and detection of a Euclidean perturbation of an independent stationary process. (English) Zbl 0592.60033

Steele, J. Michael

Ann. Probab. 14, 326-335 (1986).

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

MSC:

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

Keywords:

Kakutani’s product theorem; Hellinger integrals; Euclidean rigid motions; singular or absolutely continuous; Necessary and sufficient conditions of absolute continuity; Fisher information