Stability of the sufficient statistic “the value of the observation in the last moment” for a family of random processes with independent increments
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One investigates the problem of the stability of the sufficiency property of the statistic “the value in the last moment” for processes with independent increments relative to small perturbations of the Poisson spectra of these processes.
KeywordsRandom Process Small Perturbation Independent Increment Sufficiency Property Poisson Spectrum
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- 1.I. I. Gikhman, A. V. Skorokhod, and M. I. Yadrenko, Theory of Probability and Mathematical Statistics [in Russian], Vishcha Shkola, Kiev (1979).Google Scholar
- 2.E. B. Dynkin, “Necessary and sufficient statistics for families of probability distributions,” Usp. Mat. Nauk,6, No. 1, 68–91 (1951).Google Scholar
- 3.V. S. Mikhalevich, “On a simple sufficient statistic of unlimited divisible processes,” in: Collection of Works in Computational Mathematics and Technology, Vol. 1, Kiev (1961).Google Scholar
- 4.Nguyen Kong Shi, “The sufficiency of statistics for families of random processes with independent increments,” Candidate's Dissertation, Leningrad (1980).Google Scholar
- 5.N. A. Sapogov, “The stability of solutions of functional equations that are connected with characterization problems of probability distributions,” J. Sov. Math.,16, No. 2 (1981).Google Scholar
- 6.A. V. Skorokhod, Random Processes with Independent Increments [in Russian], Nauka, Moscow (1964).Google Scholar