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On a random system with complete connections associated with the continued fraction to the nearer integer expansion. (English) Zbl 0576.60100
The metric properties of the continued-fraction-to-the-nearer-integer expansion have been studied by G. J. Rieger [Manuscr. Math. 24, 437-448 (1978; Zbl 0377.10028); J. Reine Angew. Math. 310, 171-181 (1979; Zbl 0409.10038)] and A. M. Rockett [Acta Arith. 38, 97-103 (1980; Zbl 0368.10039)]. The present author shows that these properties can be obtained as corollaries of random-system-with-complete-connections theory [see e.g. Ş. Grigorescu and the reviewer, ”Dependence with complete connections and its applications.” Bucureşti, Ed. Ştiinţifică şi Enciclopedică, (Romanian) (1982), chapter 3]. A similar treatment for the continued fraction expansion motivating the author’s approach has been given by the reviewer, Progress in Statistics, Europ. Meeting Budapest 1972, Colloq. Math. Soc. János Bolyai 9, 335-363 (1974; Zbl 0299.60077).
Reviewer: M.Iosifescu

MSC:
60K99 Special processes
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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