Electronic Resource
Springer
Probability theory and related fields
64 (1983), S. 67-123
ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Let {X j} be i.i.d. r.v.'s taking values in a separable Banach space, and let $$s_n = \sum\limits_{j = 1}^n {X_j } $$ . The almost sure limiting behavior of the normalized random set of increments {b n −1 (S k+h-Sk): 1≦k≦n, 1≦h≦an} for a broad class of sequences a n→∞ with corresponding normalizations b n is determined. When a n/log n→∞, the results generalize and improve some recent work of Csörgő and Révész and some previous work of Lai. When a n =clog n, the results generalize and refine in a certain sense the Erdös-Rényi law of large numbers. The case a n/logn→0 is also studied.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00532594
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