Title
A functional limit theorem for Erdös and Rényi's law of large numbers
Document Type
Article
Publication Title
Probability Theory and Related Fields
Publication Date
3-1-1994
Abstract
We use the theory of large deviations on function spaces to extend Erdös and Rényi's law of large numbers. In particular, we show that with probability 1, the double-indexed set of paths {WN, n} defined by {Mathematical expression} where {Mathematical expression}, {Xi:i≧1} is an iid sequence of random variables, and h(N)=[clog N] is relatively compact; the limit set is given by the set [x:I*(x)≦1/c] where I*(x) = ∫01I(x′(t))dt and I is Cramér's rate function. © 1994 Springer-Verlag.
Volume
98
Issue
1
First Page
1
Last Page
5
DOI
10.1007/BF01311345
ISSN
01788051
E-ISSN
14322064
Recommended Citation
Sanchis, Gabriela R., "A functional limit theorem for Erdös and Rényi's law of large numbers" (1994). Faculty Publications. 1536.
https://jayscholar.etown.edu/facpubharvest/1536
