Geodesic
Karamata's Characterization Theorem, Feller, and Regular Variation in Probability Theory
Publications de l'Institut Mathématique, _N_S_71 (2002) no. 85, p. 79
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

Karamata's Characterization Theorem provided the impetus for Feller's (1966) exposition of the theory of regularly varying functions within a probability theory context. We investigate the conditions under which this theorem holds, and indicate manifestations in the identification of the spectral functions of the stable laws. Regular variation of a distribution function occurred implicitly as a necessary and sufficient condition for convergence in the 1930's, in the probabilistic work of P. Lévy, Khinchin, and Feller; and more transparently in that of Gnedenko and of Doeblin. Explicit recognition of the relevance of the concept in probability was interrupted by World War 2. A final section of this paper traces the evolution of Feller's name and early mathematical career from his Balkan origins, with a view to illuminating his recognition of the relevance of regular variation and his connection with Karamata.
DOI : 10.2298/PIM0271079S
Classification : 26A12 60F05 01A60 60-03
Keywords: characterization, boundedness on finite intervals, regularly varying functions, limit theorems in probability theory, necessary and sufficient conditions, central limit problem, history and biography 
@article{10_2298_PIM0271079S,
     author = {E. Seneta},
     title = {Karamata's {Characterization} {Theorem,} {Feller,} and {Regular} {Variation} in {Probability} {Theory}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {79 },
     year = {2002},
     volume = {_N_S_71},
     number = {85},
     doi = {10.2298/PIM0271079S},
     zbl = {1088.60008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0271079S/}
}
TY  - JOUR
AU  - E. Seneta
TI  - Karamata's Characterization Theorem, Feller, and Regular Variation in Probability Theory
JO  - Publications de l'Institut Mathématique
PY  - 2002
SP  - 79 
VL  - _N_S_71
IS  - 85
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0271079S/
DO  - 10.2298/PIM0271079S
LA  - en
ID  - 10_2298_PIM0271079S
ER  - 
%0 Journal Article
%A E. Seneta
%T Karamata's Characterization Theorem, Feller, and Regular Variation in Probability Theory
%J Publications de l'Institut Mathématique
%D 2002
%P 79 
%V _N_S_71
%N 85
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0271079S/
%R 10.2298/PIM0271079S
%G en
%F 10_2298_PIM0271079S
E. Seneta. Karamata's Characterization Theorem, Feller, and Regular Variation in Probability Theory. Publications de l'Institut Mathématique, _N_S_71 (2002) no. 85, p. 79 . doi: 10.2298/PIM0271079S

Cité par Sources :