Regular variation and probability: The early years

It is a pleasure for Bingham of Bingham, Goldie and Teugels to write in appreciation of Teugels of Bingham, Goldie and Teugels, on the occasion of Jef Teugels’ retirement, and also to remind myself of the promise we made each other—all those years ago, in the early 1970s—to write the book that regul...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 200; no. 1; pp. 357 - 363
Main Author Bingham, N.H.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.03.2007
Elsevier
Subjects
Online AccessGet full text

Cover

Loading…
Abstract It is a pleasure for Bingham of Bingham, Goldie and Teugels to write in appreciation of Teugels of Bingham, Goldie and Teugels, on the occasion of Jef Teugels’ retirement, and also to remind myself of the promise we made each other—all those years ago, in the early 1970s—to write the book that regular variation so obviously required. The theme has continued to attract my interest, Jef's and that of his pupils since. As for the book (BGT below), it continues to be my most cited work, and to find its place in the working library of probabilists. It is a pleasure also to return to the theme of Bingham [5], with the benefit of another 15 years’ worth of hindsight.
AbstractList It is a pleasure for Bingham of Bingham, Goldie and Teugels to write in appreciation of Teugels of Bingham, Goldie and Teugels, on the occasion of Jef Teugels’ retirement, and also to remind myself of the promise we made each other—all those years ago, in the early 1970s—to write the book that regular variation so obviously required. The theme has continued to attract my interest, Jef's and that of his pupils since. As for the book (BGT below), it continues to be my most cited work, and to find its place in the working library of probabilists. It is a pleasure also to return to the theme of Bingham [5], with the benefit of another 15 years’ worth of hindsight.
It is a pleasure for Bingham of Bingham, Goldie and Teugels to write in appreciation of Teugels of Bingham, Goldie and Teugels, on the occasion of Jef Teugels'retirement, and also to remind myself of the promise we made each other-all those years ago, in the early 1970s-to write the book that regular variation so obviously required. The theme has continued to attract my interest, Jef's and that of his pupils since. As for the book (BGT below), it continues to be my most cited work, and to find its place in the working library of probabilists. It is a pleasure also to return to the theme of Bingham [5], with the benefit of another 15 years' worth of hindsight.
Author Bingham, N.H.
Author_xml – sequence: 1
  givenname: N.H.
  surname: Bingham
  fullname: Bingham, N.H.
  email: nick.bingham@sheffield.ac.uk
  organization: Department of Probability and Statistics, University of Sheffield, Sheffield S3 7RH, UK
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18403129$$DView record in Pascal Francis
BookMark eNp9kM1OwzAQhC1UJNrCA3DLBW4JaydxEjihij-pEhIqZ2ttb8BVmhQ7rZS3J1UrceM0l5nZ2W_GJm3XEmPXHBIOXN6tE4ObRADkCecJpNkZm_KyqGJeFOWETSEtihgyUVywWQhrAJAVz6ZMfNDXrkEf7dE77F3XRtjaaOs7jdo1rh_uo9U3RYS-GaJhlHDJzmtsAl2ddM4-n59Wi9d4-f7ytnhcxiYD3sekJdemIgCiujC1FSilJV0BUm51aXVOUqAQMgNdYmEyaY0FypFKbfMqnbPbY-845mdHoVcbFww1DbbU7YISVQoyk2I08qPR-C4ET7XaerdBPygO6kBHrdVIRx3oKM7VSGfM3JzKMRhsao-tceEvWGaQcnEY8XD00fjp3pFXwThqDVnnyfTKdu6fK792mnxN
CODEN JCAMDI
CitedBy_id crossref_primary_10_1016_j_indag_2013_05_002
crossref_primary_10_1063_1_3270389
crossref_primary_10_3141_2106_15
crossref_primary_10_1016_j_hm_2017_12_001
crossref_primary_10_3390_axioms13020085
crossref_primary_10_1007_s42519_020_00128_1
crossref_primary_10_1016_j_jmaa_2009_04_061
crossref_primary_10_1080_17442500701830365
crossref_primary_10_4213_tvp4492
crossref_primary_10_1137_S0040585X97986369
Cites_doi 10.1017/S0305004100015681
10.2307/1426224
10.1016/0022-247X(69)90041-9
10.1007/BF00668456
10.2307/1426407
10.1515/crll.1931.164.27
10.1007/BF01218878
10.1017/S1446788700012635
10.1137/1116067
10.1137/1101027
10.1088/1469-7688/3/6/302
10.2307/1968974
10.1111/j.1467-9574.1990.tb01526.x
10.1088/1469-7688/2/4/201
10.2298/PIM0271079S
10.4064/sm-9-1-71-96
ContentType Journal Article
Copyright 2006 Elsevier B.V.
2007 INIST-CNRS
Copyright_xml – notice: 2006 Elsevier B.V.
– notice: 2007 INIST-CNRS
DBID 6I.
AAFTH
IQODW
AAYXX
CITATION
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
DOI 10.1016/j.cam.2005.11.034
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
Pascal-Francis
CrossRef
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
ProQuest Computer Science Collection
Civil Engineering Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Civil Engineering Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Civil Engineering Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1879-1778
EndPage 363
ExternalDocumentID 10_1016_j_cam_2005_11_034
18403129
S0377042706000203
GroupedDBID --K
--M
-~X
.~1
0R~
1B1
1RT
1~.
1~5
29K
4.4
457
4G.
5GY
5VS
6I.
7-5
71M
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAFWJ
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
ABAOU
ABEFU
ABFNM
ABJNI
ABMAC
ABTAH
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ADBBV
ADEZE
ADMUD
AEBSH
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CS3
D-I
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
HVGLF
HZ~
IHE
IXB
J1W
KOM
LG9
M26
M41
MHUIS
MO0
N9A
NCXOZ
NHB
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SEW
SPC
SPCBC
SSW
SSZ
T5K
TN5
UPT
WUQ
XPP
YQT
ZMT
ZY4
~02
~G-
08R
ABPIF
IQODW
0SF
AAXKI
AAYXX
ADVLN
AFJKZ
AKRWK
CITATION
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
ID FETCH-LOGICAL-c401t-eb61bc9e00eef7cfd2a66deb90ae5db8db5e62a22640b8a7c46dcd0e5ae8bd593
IEDL.DBID IXB
ISSN 0377-0427
IngestDate Sat Oct 26 01:15:15 EDT 2024
Thu Sep 26 17:39:20 EDT 2024
Sun Oct 22 16:03:56 EDT 2023
Fri Feb 23 02:30:16 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Keywords Tauberian theory
Probability theory
Regular variation
Probability distribution
Numerical analysis
Applied mathematics
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c401t-eb61bc9e00eef7cfd2a66deb90ae5db8db5e62a22640b8a7c46dcd0e5ae8bd593
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
OpenAccessLink https://www.sciencedirect.com/science/article/pii/S0377042706000203
PQID 29306462
PQPubID 23500
PageCount 7
ParticipantIDs proquest_miscellaneous_29306462
crossref_primary_10_1016_j_cam_2005_11_034
pascalfrancis_primary_18403129
elsevier_sciencedirect_doi_10_1016_j_cam_2005_11_034
PublicationCentury 2000
PublicationDate 2007-03-01
PublicationDateYYYYMMDD 2007-03-01
PublicationDate_xml – month: 03
  year: 2007
  text: 2007-03-01
  day: 01
PublicationDecade 2000
PublicationPlace Amsterdam
PublicationPlace_xml – name: Amsterdam
PublicationTitle Journal of computational and applied mathematics
PublicationYear 2007
Publisher Elsevier B.V
Elsevier
Publisher_xml – name: Elsevier B.V
– name: Elsevier
References W. Feller, An Introduction to Probability Theory and its Applications, third ed., vol. I, Wiley, 1968 (first ed., 1950, second ed., 1957).
Seneta (bib47) 1976; vol. 508
Karamata (bib27) 1930; 4
Khintchine (bib29) 1935; 6
Lévy (bib34) 1937
G.H. Hardy, Orders of infinity: The ‘infinitärcalcül’ of Paul du Bois-Reymond, Cambridge Tracts in Math. vol. 12, Cambridge University Press, Cambridge, 1910 (second ed., 1924).
Pólya, Szegö (bib41) 1925
Maller (bib35) 1978; 43
Seneta (bib48) 1990; 48
Bingham, Goldie, Teugels (bib7) 1987
Seneta (bib49) 2002; 71
Feller (bib15) 1935; 40
G. Pólya, Über eine neue Weise, bestimmte Integrale in der analytischen Zahlentheorie zu gebrauchen, Göttinger Nachr. (1917) 149–159.
Fréchet (bib19) 1937; 6
Seneta (bib45) 1969; 1
Seneta (bib46) 1974; 6
Adler, Feldman, Taqqu (bib1) 1998
Chung (bib11) 1968
Beran (bib3) 1994
Mejzler (bib39) 1949; 12
Gnedenko (bib22) 1943; 44
Gnedenko, Kolmogorov (bib23) 1954
Leadbetter, Lindgren, Rootzén (bib32) 1983
Bingham (bib5) 1990; 48
Breiman (bib10) 1968
Fisher, Tippett (bib18) 1928; 24
Bingham, Kiesel, Schmidt (bib9) 2003; 3
Korevaar (bib30) 2004
E. Landau, Sur les valeurs moyennes de certaines fonctions arithmétiques, Bull. Acad. R. Belgique (1911) 443–472.
Karamata (bib28) 1931; 164
Resnick (bib42) 1987
Bingham, Kiesel (bib8) 2002; 2
Geluk, de Haan (bib20) 1987; vol. 40
Bingham (bib6) 1990; 22
F. Bassi, P. Embrechts, M. Kafetzaki, Risk Management and Quantile Estimation. in: Adler, et al., 1998, pp. 111–130.
Ehrenfeucht, Fisz (bib13) 1960; 9
Maller (bib36) 1979; 28
Billingsley (bib4) 1979
Sakovich (bib44) 1956; 1
Meerschaert, Scheffler (bib38) 2001
Gnedenko (bib21) 1939; 30
Embrechts, Klüppelberg, Mikosch (bib14) 1997
de Haan (bib25) 1990; 44
Marcus, Pinsky (bib37) 1969; 28
de Haan (bib24) 1970; vol. 32
Doeblin (bib12) 1940; 9
Lévy (bib33) 1935; 14
Rogozin (bib43) 1976; 16
W. Feller, An Introduction to Probability Theory and its Applications, second ed., vol. II, Wiley, 1971 (first ed., 1966).
de Haan (10.1016/j.cam.2005.11.034_bib24) 1970; vol. 32
Gnedenko (10.1016/j.cam.2005.11.034_bib23) 1954
Korevaar (10.1016/j.cam.2005.11.034_bib30) 2004
Billingsley (10.1016/j.cam.2005.11.034_bib4) 1979
Karamata (10.1016/j.cam.2005.11.034_bib27) 1930; 4
10.1016/j.cam.2005.11.034_bib2
Pólya (10.1016/j.cam.2005.11.034_bib41) 1925
Maller (10.1016/j.cam.2005.11.034_bib35) 1978; 43
Resnick (10.1016/j.cam.2005.11.034_bib42) 1987
Bingham (10.1016/j.cam.2005.11.034_bib5) 1990; 48
10.1016/j.cam.2005.11.034_bib40
Sakovich (10.1016/j.cam.2005.11.034_bib44) 1956; 1
Beran (10.1016/j.cam.2005.11.034_bib3) 1994
Gnedenko (10.1016/j.cam.2005.11.034_bib21) 1939; 30
Fréchet (10.1016/j.cam.2005.11.034_bib19) 1937; 6
Ehrenfeucht (10.1016/j.cam.2005.11.034_bib13) 1960; 9
Bingham (10.1016/j.cam.2005.11.034_bib7) 1987
Fisher (10.1016/j.cam.2005.11.034_bib18) 1928; 24
Rogozin (10.1016/j.cam.2005.11.034_bib43) 1976; 16
10.1016/j.cam.2005.11.034_bib17
10.1016/j.cam.2005.11.034_bib16
Feller (10.1016/j.cam.2005.11.034_bib15) 1935; 40
Khintchine (10.1016/j.cam.2005.11.034_bib29) 1935; 6
Bingham (10.1016/j.cam.2005.11.034_bib6) 1990; 22
Geluk (10.1016/j.cam.2005.11.034_bib20) 1987; vol. 40
Karamata (10.1016/j.cam.2005.11.034_bib28) 1931; 164
Seneta (10.1016/j.cam.2005.11.034_bib47) 1976; vol. 508
Adler (10.1016/j.cam.2005.11.034_bib1) 1998
Chung (10.1016/j.cam.2005.11.034_bib11) 1968
10.1016/j.cam.2005.11.034_bib26
Bingham (10.1016/j.cam.2005.11.034_bib8) 2002; 2
Leadbetter (10.1016/j.cam.2005.11.034_bib32) 1983
Lévy (10.1016/j.cam.2005.11.034_bib33) 1935; 14
Marcus (10.1016/j.cam.2005.11.034_bib37) 1969; 28
Doeblin (10.1016/j.cam.2005.11.034_bib12) 1940; 9
Seneta (10.1016/j.cam.2005.11.034_bib45) 1969; 1
Bingham (10.1016/j.cam.2005.11.034_bib9) 2003; 3
Mejzler (10.1016/j.cam.2005.11.034_bib39) 1949; 12
Gnedenko (10.1016/j.cam.2005.11.034_bib22) 1943; 44
Maller (10.1016/j.cam.2005.11.034_bib36) 1979; 28
Seneta (10.1016/j.cam.2005.11.034_bib49) 2002; 71
10.1016/j.cam.2005.11.034_bib31
Embrechts (10.1016/j.cam.2005.11.034_bib14) 1997
Breiman (10.1016/j.cam.2005.11.034_bib10) 1968
Meerschaert (10.1016/j.cam.2005.11.034_bib38) 2001
Seneta (10.1016/j.cam.2005.11.034_bib48) 1990; 48
de Haan (10.1016/j.cam.2005.11.034_bib25) 1990; 44
Lévy (10.1016/j.cam.2005.11.034_bib34) 1937
Seneta (10.1016/j.cam.2005.11.034_bib46) 1974; 6
References_xml – volume: 6
  start-page: 93
  year: 1937
  end-page: 116
  ident: bib19
  article-title: Sur la loi de probabilité de l’écart maximum
  publication-title: Ann. Soc. Math. Polon.
  contributor:
    fullname: Fréchet
– year: 1925
  ident: bib41
  article-title: Aufgaben und Lehrsätze aus der Analysis, I, II
  contributor:
    fullname: Szegö
– volume: 14
  start-page: 347
  year: 1935
  end-page: 402
  ident: bib33
  article-title: Propriétés asymptotiques des sommes des variables aléatoires indépendantes ou enchainées
  publication-title: J. Math. Pures Appl.
  contributor:
    fullname: Lévy
– year: 1998
  ident: bib1
  article-title: A Practical Guide to Heavy Tails
  contributor:
    fullname: Taqqu
– volume: 2
  start-page: 241
  year: 2002
  end-page: 250
  ident: bib8
  article-title: Semi-parametric modelling in finance: theoretical foundations
  publication-title: Quantitative Finance
  contributor:
    fullname: Kiesel
– volume: 30
  start-page: 61
  year: 1939
  end-page: 81
  ident: bib21
  article-title: On the theory of domains of attraction for stable laws (Russian)
  publication-title: Gos. Univ. Uch. Zap. Mat.
  contributor:
    fullname: Gnedenko
– year: 1997
  ident: bib14
  article-title: Modelling Extremal Events
  contributor:
    fullname: Mikosch
– year: 1987
  ident: bib42
  article-title: Extreme Values, Regular Variation and Point Processes
  contributor:
    fullname: Resnick
– volume: 9
  start-page: 17
  year: 1960
  end-page: 19
  ident: bib13
  article-title: A necessary and sufficient condition for the validity of the weak law of large numbers
  publication-title: Bull. Acad. Pol. Sci.
  contributor:
    fullname: Fisz
– volume: 44
  start-page: 423
  year: 1943
  end-page: 453
  ident: bib22
  article-title: Sur la distribution limite du terme maximum d’une série aléatoire
  publication-title: Ann. Math.
  contributor:
    fullname: Gnedenko
– volume: 4
  start-page: 38
  year: 1930
  end-page: 53
  ident: bib27
  article-title: Sur un mode de croissance régulière des fonctions
  publication-title: Mathematica (Cluj)
  contributor:
    fullname: Karamata
– volume: 40
  start-page: 521
  year: 1935
  end-page: 559
  ident: bib15
  article-title: Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung
  publication-title: Math. Z.
  contributor:
    fullname: Feller
– volume: 43
  start-page: 141
  year: 1978
  end-page: 148
  ident: bib35
  article-title: Relative stability and the strong law of large numbers
  publication-title: Z. Wahrschein.
  contributor:
    fullname: Maller
– volume: 1
  start-page: 322
  year: 1956
  end-page: 325
  ident: bib44
  article-title: A single form for the conditions for attraction to stable laws
  publication-title: Theory Prob. Its Appl.
  contributor:
    fullname: Sakovich
– year: 1994
  ident: bib3
  article-title: Statistics of Long-Memory Processes
  contributor:
    fullname: Beran
– year: 2004
  ident: bib30
  article-title: Tauberian Theory, A Century of Developments
  contributor:
    fullname: Korevaar
– volume: vol. 508
  year: 1976
  ident: bib47
  publication-title: Regularly Varying Functions, Lecture Notes in Mathematics
  contributor:
    fullname: Seneta
– volume: 164
  start-page: 27
  year: 1931
  end-page: 39
  ident: bib28
  article-title: Neuer Beweis und Verallgemeinerung der Tauberschen Sätze, welche die Laplacessche und Stieltjessche Transformationen betreffen
  publication-title: J. Reine Angew. Math.
  contributor:
    fullname: Karamata
– volume: 28
  start-page: 440
  year: 1969
  end-page: 449
  ident: bib37
  article-title: On the domain of attraction of
  publication-title: J. Math. Anal. Appl.
  contributor:
    fullname: Pinsky
– year: 1937
  ident: bib34
  article-title: Théorie de l’addition des variables aléatoires
  contributor:
    fullname: Lévy
– volume: 48
  start-page: 169
  year: 1990
  end-page: 180
  ident: bib5
  article-title: Regular variation in probability theory
  publication-title: Publ. Inst. Math. Beograd
  contributor:
    fullname: Bingham
– volume: 16
  start-page: 575
  year: 1976
  end-page: 595
  ident: bib43
  article-title: Relatively stable random walks
  publication-title: Theory Probab. Its. Appl.
  contributor:
    fullname: Rogozin
– volume: 12
  start-page: 31
  year: 1949
  end-page: 35
  ident: bib39
  article-title: On a theorem of B.V. Gnedenko (Russian)
  publication-title: Sb. T. Inst. Mat. Akad. Nauk Ukr. RSR
  contributor:
    fullname: Mejzler
– year: 1983
  ident: bib32
  article-title: Extremes and Related Properties of Random Sequences and Processes
  contributor:
    fullname: Rootzén
– volume: 71
  start-page: 79
  year: 2002
  end-page: 89
  ident: bib49
  article-title: Karamata's characterization theorem, Feller, and regular variation in probability theory
  publication-title: Publ. Inst. Math. Beograd
  contributor:
    fullname: Seneta
– year: 1987
  ident: bib7
  article-title: Regular Variation
  contributor:
    fullname: Teugels
– volume: 28
  start-page: 499
  year: 1979
  end-page: 509
  ident: bib36
  article-title: Relative stability, characteristic functions and stochastic compactness
  publication-title: J. Austr. Math. Soc. A
  contributor:
    fullname: Maller
– year: 1979
  ident: bib4
  article-title: Probability and Measure
  contributor:
    fullname: Billingsley
– volume: 44
  start-page: 45
  year: 1990
  end-page: 68
  ident: bib25
  article-title: Fighting the arch-enemy with mathematics
  publication-title: Stat. Neerl.
  contributor:
    fullname: de Haan
– volume: 6
  start-page: 371
  year: 1935
  end-page: 393
  ident: bib29
  article-title: Sul dominio di attrazione della legge di Gauss
  publication-title: G. Ist. Ital. Attuari
  contributor:
    fullname: Khintchine
– volume: 3
  start-page: 426
  year: 2003
  end-page: 441
  ident: bib9
  article-title: A semi-parametric approach to risk management
  publication-title: Quantitative Finance
  contributor:
    fullname: Schmidt
– year: 1954
  ident: bib23
  article-title: Limit distributions for sums of independent random variables (Russian)
  contributor:
    fullname: Kolmogorov
– volume: 9
  start-page: 71
  year: 1940
  end-page: 96
  ident: bib12
  article-title: Sur l’ensemble des puissances d’une loi de probabilité
  publication-title: Studia Math.
  contributor:
    fullname: Doeblin
– year: 1968
  ident: bib11
  article-title: A Course in Probability Theory
  contributor:
    fullname: Chung
– volume: 24
  start-page: 180
  year: 1928
  end-page: 190
  ident: bib18
  article-title: Limiting forms of the frequency distribution of the largest or smallest member of a sample
  publication-title: Proc. Cambridge Phil. Soc.
  contributor:
    fullname: Tippett
– volume: 48
  start-page: 45
  year: 1990
  end-page: 51
  ident: bib48
  article-title: Karamata's iteration theory and normed regularly varying sequences in a historical light
  publication-title: Publ. Inst. Math. Beograd
  contributor:
    fullname: Seneta
– year: 2001
  ident: bib38
  article-title: Limit Distributions for Sums of Independent Random Vectors. Heavy Tails in Theory and Practice
  contributor:
    fullname: Scheffler
– volume: 1
  start-page: 1
  year: 1969
  end-page: 42
  ident: bib45
  article-title: Functional equations and the Galton-Watson process
  publication-title: Advances Appl. Probab.
  contributor:
    fullname: Seneta
– volume: 22
  start-page: 51
  year: 1990
  end-page: 58
  ident: bib6
  article-title: Kolmogorov's work on probability
  publication-title: particularly limit theorems, Bull. London Math. Soc.
  contributor:
    fullname: Bingham
– volume: 6
  start-page: 408
  year: 1974
  end-page: 420
  ident: bib46
  article-title: Regularly varying functions in the theory of simple branching processes
  publication-title: Advances Appl. Probab.
  contributor:
    fullname: Seneta
– year: 1968
  ident: bib10
  article-title: Probability
  contributor:
    fullname: Breiman
– volume: vol. 32
  year: 1970
  ident: bib24
  publication-title: On Regular Variation and its Application to the Weak Convergence of Sample extremes, Math. Centre Tracts
  contributor:
    fullname: de Haan
– volume: vol. 40
  year: 1987
  ident: bib20
  publication-title: Regular Variation, Extensions and Tauberian Theorems, CWI Tracts
  contributor:
    fullname: de Haan
– volume: 24
  start-page: 180
  year: 1928
  ident: 10.1016/j.cam.2005.11.034_bib18
  article-title: Limiting forms of the frequency distribution of the largest or smallest member of a sample
  publication-title: Proc. Cambridge Phil. Soc.
  doi: 10.1017/S0305004100015681
  contributor:
    fullname: Fisher
– volume: vol. 508
  year: 1976
  ident: 10.1016/j.cam.2005.11.034_bib47
  contributor:
    fullname: Seneta
– year: 1968
  ident: 10.1016/j.cam.2005.11.034_bib10
  contributor:
    fullname: Breiman
– volume: 6
  start-page: 408
  year: 1974
  ident: 10.1016/j.cam.2005.11.034_bib46
  article-title: Regularly varying functions in the theory of simple branching processes
  publication-title: Advances Appl. Probab.
  doi: 10.2307/1426224
  contributor:
    fullname: Seneta
– volume: 6
  start-page: 371
  year: 1935
  ident: 10.1016/j.cam.2005.11.034_bib29
  article-title: Sul dominio di attrazione della legge di Gauss
  publication-title: G. Ist. Ital. Attuari
  contributor:
    fullname: Khintchine
– volume: 12
  start-page: 31
  year: 1949
  ident: 10.1016/j.cam.2005.11.034_bib39
  article-title: On a theorem of B.V. Gnedenko (Russian)
  publication-title: Sb. T. Inst. Mat. Akad. Nauk Ukr. RSR
  contributor:
    fullname: Mejzler
– ident: 10.1016/j.cam.2005.11.034_bib2
– volume: 48
  start-page: 169
  issue: 62
  year: 1990
  ident: 10.1016/j.cam.2005.11.034_bib5
  article-title: Regular variation in probability theory
  publication-title: Publ. Inst. Math. Beograd
  contributor:
    fullname: Bingham
– volume: 6
  start-page: 93
  year: 1937
  ident: 10.1016/j.cam.2005.11.034_bib19
  article-title: Sur la loi de probabilité de l’écart maximum
  publication-title: Ann. Soc. Math. Polon.
  contributor:
    fullname: Fréchet
– volume: 30
  start-page: 61
  issue: 3
  year: 1939
  ident: 10.1016/j.cam.2005.11.034_bib21
  article-title: On the theory of domains of attraction for stable laws (Russian)
  publication-title: Gos. Univ. Uch. Zap. Mat.
  contributor:
    fullname: Gnedenko
– volume: vol. 32
  year: 1970
  ident: 10.1016/j.cam.2005.11.034_bib24
  contributor:
    fullname: de Haan
– volume: 4
  start-page: 38
  year: 1930
  ident: 10.1016/j.cam.2005.11.034_bib27
  article-title: Sur un mode de croissance régulière des fonctions
  publication-title: Mathematica (Cluj)
  contributor:
    fullname: Karamata
– volume: 28
  start-page: 440
  year: 1969
  ident: 10.1016/j.cam.2005.11.034_bib37
  article-title: On the domain of attraction of exp(-e-x)
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/0022-247X(69)90041-9
  contributor:
    fullname: Marcus
– year: 1987
  ident: 10.1016/j.cam.2005.11.034_bib42
  contributor:
    fullname: Resnick
– volume: 14
  start-page: 347
  issue: 8
  year: 1935
  ident: 10.1016/j.cam.2005.11.034_bib33
  article-title: Propriétés asymptotiques des sommes des variables aléatoires indépendantes ou enchainées
  publication-title: J. Math. Pures Appl.
  contributor:
    fullname: Lévy
– year: 1925
  ident: 10.1016/j.cam.2005.11.034_bib41
  contributor:
    fullname: Pólya
– year: 1994
  ident: 10.1016/j.cam.2005.11.034_bib3
  contributor:
    fullname: Beran
– volume: 43
  start-page: 141
  year: 1978
  ident: 10.1016/j.cam.2005.11.034_bib35
  article-title: Relative stability and the strong law of large numbers
  publication-title: Z. Wahrschein.
  doi: 10.1007/BF00668456
  contributor:
    fullname: Maller
– year: 1968
  ident: 10.1016/j.cam.2005.11.034_bib11
  contributor:
    fullname: Chung
– volume: 1
  start-page: 1
  year: 1969
  ident: 10.1016/j.cam.2005.11.034_bib45
  article-title: Functional equations and the Galton-Watson process
  publication-title: Advances Appl. Probab.
  doi: 10.2307/1426407
  contributor:
    fullname: Seneta
– volume: 48
  start-page: 45
  issue: 62
  year: 1990
  ident: 10.1016/j.cam.2005.11.034_bib48
  article-title: Karamata's iteration theory and normed regularly varying sequences in a historical light
  publication-title: Publ. Inst. Math. Beograd
  contributor:
    fullname: Seneta
– volume: 164
  start-page: 27
  year: 1931
  ident: 10.1016/j.cam.2005.11.034_bib28
  article-title: Neuer Beweis und Verallgemeinerung der Tauberschen Sätze, welche die Laplacessche und Stieltjessche Transformationen betreffen
  publication-title: J. Reine Angew. Math.
  doi: 10.1515/crll.1931.164.27
  contributor:
    fullname: Karamata
– volume: 40
  start-page: 521
  year: 1935
  ident: 10.1016/j.cam.2005.11.034_bib15
  article-title: Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung
  publication-title: Math. Z.
  doi: 10.1007/BF01218878
  contributor:
    fullname: Feller
– volume: 9
  start-page: 17
  year: 1960
  ident: 10.1016/j.cam.2005.11.034_bib13
  article-title: A necessary and sufficient condition for the validity of the weak law of large numbers
  publication-title: Bull. Acad. Pol. Sci.
  contributor:
    fullname: Ehrenfeucht
– ident: 10.1016/j.cam.2005.11.034_bib17
– volume: 28
  start-page: 499
  year: 1979
  ident: 10.1016/j.cam.2005.11.034_bib36
  article-title: Relative stability, characteristic functions and stochastic compactness
  publication-title: J. Austr. Math. Soc. A
  doi: 10.1017/S1446788700012635
  contributor:
    fullname: Maller
– year: 1987
  ident: 10.1016/j.cam.2005.11.034_bib7
  contributor:
    fullname: Bingham
– volume: 16
  start-page: 575
  year: 1976
  ident: 10.1016/j.cam.2005.11.034_bib43
  article-title: Relatively stable random walks
  publication-title: Theory Probab. Its. Appl.
  doi: 10.1137/1116067
  contributor:
    fullname: Rogozin
– year: 1997
  ident: 10.1016/j.cam.2005.11.034_bib14
  contributor:
    fullname: Embrechts
– ident: 10.1016/j.cam.2005.11.034_bib40
– year: 2004
  ident: 10.1016/j.cam.2005.11.034_bib30
  contributor:
    fullname: Korevaar
– year: 1998
  ident: 10.1016/j.cam.2005.11.034_bib1
  contributor:
    fullname: Adler
– volume: 22
  start-page: 51
  year: 1990
  ident: 10.1016/j.cam.2005.11.034_bib6
  article-title: Kolmogorov's work on probability
  publication-title: particularly limit theorems, Bull. London Math. Soc.
  contributor:
    fullname: Bingham
– volume: 1
  start-page: 322
  year: 1956
  ident: 10.1016/j.cam.2005.11.034_bib44
  article-title: A single form for the conditions for attraction to stable laws
  publication-title: Theory Prob. Its Appl.
  doi: 10.1137/1101027
  contributor:
    fullname: Sakovich
– volume: 3
  start-page: 426
  year: 2003
  ident: 10.1016/j.cam.2005.11.034_bib9
  article-title: A semi-parametric approach to risk management
  publication-title: Quantitative Finance
  doi: 10.1088/1469-7688/3/6/302
  contributor:
    fullname: Bingham
– volume: 44
  start-page: 423
  year: 1943
  ident: 10.1016/j.cam.2005.11.034_bib22
  article-title: Sur la distribution limite du terme maximum d’une série aléatoire
  publication-title: Ann. Math.
  doi: 10.2307/1968974
  contributor:
    fullname: Gnedenko
– volume: 44
  start-page: 45
  year: 1990
  ident: 10.1016/j.cam.2005.11.034_bib25
  article-title: Fighting the arch-enemy with mathematics
  publication-title: Stat. Neerl.
  doi: 10.1111/j.1467-9574.1990.tb01526.x
  contributor:
    fullname: de Haan
– ident: 10.1016/j.cam.2005.11.034_bib16
– year: 1937
  ident: 10.1016/j.cam.2005.11.034_bib34
  contributor:
    fullname: Lévy
– volume: 2
  start-page: 241
  year: 2002
  ident: 10.1016/j.cam.2005.11.034_bib8
  article-title: Semi-parametric modelling in finance: theoretical foundations
  publication-title: Quantitative Finance
  doi: 10.1088/1469-7688/2/4/201
  contributor:
    fullname: Bingham
– ident: 10.1016/j.cam.2005.11.034_bib31
– volume: vol. 40
  year: 1987
  ident: 10.1016/j.cam.2005.11.034_bib20
  contributor:
    fullname: Geluk
– year: 1979
  ident: 10.1016/j.cam.2005.11.034_bib4
  contributor:
    fullname: Billingsley
– volume: 71
  start-page: 79
  issue: 85
  year: 2002
  ident: 10.1016/j.cam.2005.11.034_bib49
  article-title: Karamata's characterization theorem, Feller, and regular variation in probability theory
  publication-title: Publ. Inst. Math. Beograd
  doi: 10.2298/PIM0271079S
  contributor:
    fullname: Seneta
– year: 1954
  ident: 10.1016/j.cam.2005.11.034_bib23
  contributor:
    fullname: Gnedenko
– ident: 10.1016/j.cam.2005.11.034_bib26
– year: 2001
  ident: 10.1016/j.cam.2005.11.034_bib38
  contributor:
    fullname: Meerschaert
– year: 1983
  ident: 10.1016/j.cam.2005.11.034_bib32
  contributor:
    fullname: Leadbetter
– volume: 9
  start-page: 71
  year: 1940
  ident: 10.1016/j.cam.2005.11.034_bib12
  article-title: Sur l’ensemble des puissances d’une loi de probabilité
  publication-title: Studia Math.
  doi: 10.4064/sm-9-1-71-96
  contributor:
    fullname: Doeblin
SSID ssj0006914
Score 1.9082884
Snippet It is a pleasure for Bingham of Bingham, Goldie and Teugels to write in appreciation of Teugels of Bingham, Goldie and Teugels, on the occasion of Jef Teugels’...
It is a pleasure for Bingham of Bingham, Goldie and Teugels to write in appreciation of Teugels of Bingham, Goldie and Teugels, on the occasion of Jef...
SourceID proquest
crossref
pascalfrancis
elsevier
SourceType Aggregation Database
Index Database
Publisher
StartPage 357
SubjectTerms Exact sciences and technology
General topics
Mathematics
Probability and statistics
Probability theory
Probability theory and stochastic processes
Probability theory on algebraic and topological structures
Regular variation
Sciences and techniques of general use
Tauberian theory
Title Regular variation and probability: The early years
URI https://dx.doi.org/10.1016/j.cam.2005.11.034
https://search.proquest.com/docview/29306462
Volume 200
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwEB7xuIAQAgrqQrvNgVOldL2JHwk3WIG2PLYSj2rFJfJjIlGJsGIXJC78dsZxQoUQPfQQWYls2fpij2fsmfkAdkuGNi1dEkubiphjVsa5wiw2SiJybizPfTTy2UgOr_jxWIznYNDGwni3ykb2B5leS-vmS69Bsze5ueldsFQpzxTBZLhPIzmcin4dxDc-eJXGMg_5valy7Gu3N5u1j5fVt-FYxSfyTPlHe9PKRE8JsTJQXbyT2vVWdLQGq40OGe2HYa7DHFYbsHz2moB1-gmS85pj_j56JFu4Bj_SlYs8fUxIzP20F9EMidDnN46eqJhuwtXR4eVgGDf0CLElo2gWo5F9Y3NkDLFUlgDXUjo0OdMonMmcESgT7SNlmcm0slw66xgKjZlxIk-3YKG6q_AzRKXnm6dH2URzRY01rctSaOftIaVZB763wBSTkAWjaN3D_hSEomezFGRNFIRiB3gLXfHmVxYkpf_VrPsG5r8dkQ2aklrSgW8t7gWtAX-xoSu8e5gWpLKQZiWT7f_reQeWwomt9yz7Aguz-wf8SqrGzHRh_sdzvwuL-we_T059-fNkOOrWM4zeRoPxr-sXvsXXtw
link.rule.ids 315,783,787,3513,4509,24128,27581,27936,27937,45597,45675,45691,45886
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB58HFREfOL67MGTUDa2adJ6E1HWx-7BB3gLeUxhBeviroL_3knTKiJ68FAKgSHla2Yyk5nMB3BQMrRp6ZJY2DSLOeZlXEjMYyMFIufG8sLfRu4PRO-eXz5kD1Nw2t6F8WWVje0PNr221s1It0GzOxoOu7csldIzRTAR8mnTMEveQEHaOXtycdUbfBpkGgtdpKSMvUCb3KzLvKx-Cicrvpdnyn_bnhZHekyglYHt4ofhrnej82VYatzI6CR86QpMYbUKC_3PHqzjNUhuapr5l-iNwuEa_0hXLvIMMqE39_txRIskQt_iOHqn13gd7s_P7k57ccOQEFuKiyYxGnFkbIGMIZbSEuZaCIemYBozZ3JnMhSJ9pdlmcm1tFw46xhmGnPjsiLdgJnqucJNiEpPOU-PtInmkoQ1qWaZaedDIqlZBw5bYNQoNMJQbYXYoyIUPaFlRgGFIhQ7wFvo1Le_qchQ_yW29w3mr4koDE3JM-nAfou7IjXwuQ1d4fPrWJHXQs6VSLb-N_M-zPXu-tfq-mJwtQ3z4QDXF5rtwMzk5RV3yfOYmL1mZX0AvVnWHw
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Regular+variation+and+probability%3A+The+early+years&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Bingham%2C+N.H.&rft.date=2007-03-01&rft.pub=Elsevier+B.V&rft.issn=0377-0427&rft.eissn=1879-1778&rft.volume=200&rft.issue=1&rft.spage=357&rft.epage=363&rft_id=info:doi/10.1016%2Fj.cam.2005.11.034&rft.externalDocID=S0377042706000203
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon