Regularly Varying Sequences.
PRINCETON UNIV N J DEPT OF STATISTICS
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A simple necessary and sufficient condition is developed for a sequence thetan , n 0,1,2,.... of positive terms, to satisfy thetan Rn, n or 0 , where R. is a regularly varying function on 0, infinity. The condition given in the report leads to a Karamata-type exponential representation for thetan. Various associated difficulties are also discussed. The results are of relevance in connection with limit theorems in various branches of probability theory. Author
- Statistics and Probability