Regularly Varying Sequences.

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Abstract:

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

Author(s):
Seneta, E. ; Galambos, J.
Author Organization(s):
PRINCETON UNIV N J DEPT OF STATISTICS
Descriptive Note:
Technical rept.,
Supplementary Note:
Prepared in cooperation with Temple Univ., Philadelphia, Pa. Dept. of Mathematics.
Pagination:
0016

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
TR-29-Ser-2
Contract/Grant Number(s):
N00014-67-A-0151-0017
 Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
(*SEQUENCES(MATHEMATICS), FUNCTIONS(MATHEMATICS)), CONVERGENCE, MEASURE THEORY, SET THEORY, PROBABILITY
Field(s)/Group(s):
Statistics and Probability
Keyword(s):
LIMIT THEOREMS, *PROBABILITY, IMBEDDINGS(MATHEMATICS)
Report Date:
1973 Jan 01