On the application of the individual ergodic theorem to discrete stochastic processes
نویسندگان
چکیده
منابع مشابه
On the Application of the Individual Ergodic Theorem to Discrete Stochastic Processes
That Birkhoff's individual ergodic theorem provides a strong law of large numbers for stationary stochastic processes has been known since its applications to this end by Doob (cf. [3; 4]) and Hopf [9]. The conclusion of the ergodic theorem as it applies to a sequence of random variables, {x " }, is from one point of view considerably stronger than that of the strong law of large numbers. The l...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1955
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1955-0067398-5