SUBEXPONENTIALITY AND INFINITE DIVISIBILITY

被引：227

作者：

EMBRECHTS, P

GOLDIE, CM

VERAVERBEKE, N

机构：

[1] UNIV SUSSEX, BRIGHTON BN1 9QH, E SUSSEX, ENGLAND

[2] LIMBURGS UNIV CENTRUM, DEPT WISKUNDE, B-3610 DIEPENBEEK, BELGIUM

来源：

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE | 1979年 / 49卷 / 03期

关键词：

D O I：

10.1007/BF00535504

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let ℒ denote the class of subexponential distribution functions. For F infinitely divisible on [0, ∞) with Lévy measure v, the following assertions are proved to be equivalent: (i) F∈ℒ, (ii) v(1, x]/v(1,∞)∈ℒ, (iii) 1-F(x)∼v(x, ∞) as x→∞. In the proof of this theorem, some new results on ∞ are established. © 1979 Springer-Verlag.

引用

页码：335 / 347

页数：13

共 17 条

[1]

[Anonymous], THEORY PROBAB APPL

[2]

Athreya K. B., 2012, BRANCHING PROCESSES, DOI DOI 10.1007/978-3-642-65371-1

[3]

BONDESSON L, UNPUBLISHED

[4] LEMMA ON REGULAR VARIATION OF A TRANSIENT RENEWAL FUNCTION [J].

CALLAERT, H ;

COHEN, JW .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1972, 24 (04) :275-278

[5]

Chistyakov V.P., 1964, THEORY PROBAB APPL, V9, P640, DOI DOI 10.1137/1109088

[6] DEGENERACY PROPERTIES OF SUBCRITICAL BRANCHING PROCESSES [J].

CHOVER, J ;

NEY, P ;

WAINGER, S .

ANNALS OF PROBABILITY, 1973, 1 (04) :663-673

[7] FUNCTIONS OF PROBABILITY MEASURES [J].

CHOVER, J ;

NEY, P ;

WAINGER, S .

JOURNAL D ANALYSE MATHEMATIQUE, 1973, 26 :255-302

[8] SOME RESULTS ON REGULAR VARIATION FOR DISTRIBUTIONS IN QUEUING AND FLUCTUATION THEORY [J].

COHEN, JW .

JOURNAL OF APPLIED PROBABILITY, 1973, 10 (02) :343-353

[9]

Feller W., 1969, ENSEIGN MATH, V15, P107

[10]

Feller W., 1971, An Introduction to Probability Theory and Its Applications, V2

← 1 2 →