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Let Xk, k= 1, 2, 3, • • -, be a sequence of mutually independent random variables on an appropriate probability space which have a given common distribution function F. Let Sn = Xi+ • • • +Xn, then the event lim inf | S„\ = 0 has probability either zero or one. If this event has zero chance, we say F is transient; in the other case, | 5„| tends to infinity almost surely, and F is called recurre...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1962
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1962-0139212-4