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Volumn 200, Issue 1, 2007, Pages 357-363

Regular variation and probability: The early years

Author keywords

Probability theory; Regular variation; Tauberian theory

Indexed keywords

INFORMATION DISSEMINATION; INTELLECTUAL PROPERTY; LIBRARIES; PROFESSIONAL ASPECTS;

EID: 33750964486     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.11.034     Document Type: Article
Times cited : (12)

References (49)
  • 2
    • 33750947342 scopus 로고    scopus 로고
    • F. Bassi, P. Embrechts, M. Kafetzaki, Risk Management and Quantile Estimation. in: Adler, et al., 1998, pp. 111-130.
  • 5
    • 33750943676 scopus 로고
    • Regular variation in probability theory
    • Bingham N.H. Regular variation in probability theory. Publ. Inst. Math. Beograd 48 62 (1990) 169-180
    • (1990) Publ. Inst. Math. Beograd , vol.48 , Issue.62 , pp. 169-180
    • Bingham, N.H.1
  • 6
    • 33750944969 scopus 로고
    • Kolmogorov's work on probability
    • [in: D.G. Kendall, et al., Obituary, Andrei Nikolaevich Kolmogorov, Bull. London Math. Soc. 31-100]
    • Bingham N.H. Kolmogorov's work on probability. particularly limit theorems, Bull. London Math. Soc. 22 (1990) 51-58 [in: D.G. Kendall, et al., Obituary, Andrei Nikolaevich Kolmogorov, Bull. London Math. Soc. 31-100]
    • (1990) particularly limit theorems, Bull. London Math. Soc. , vol.22 , pp. 51-58
    • Bingham, N.H.1
  • 8
    • 85008813608 scopus 로고    scopus 로고
    • Semi-parametric modelling in finance: theoretical foundations
    • Bingham N.H., and Kiesel R. Semi-parametric modelling in finance: theoretical foundations. Quantitative Finance 2 (2002) 241-250
    • (2002) Quantitative Finance , vol.2 , pp. 241-250
    • Bingham, N.H.1    Kiesel, R.2
  • 10
    • 0004256573 scopus 로고
    • Addison-Wesley, Reading, MA
    • Breiman L. Probability (1968), Addison-Wesley, Reading, MA
    • (1968) Probability
    • Breiman, L.1
  • 11
    • 0003937712 scopus 로고
    • Harcourt, Brace, Jovanovich, New York (second ed., Academic Press, New York, 1974, third ed., 2001)
    • Chung K.-L. A Course in Probability Theory (1968), Harcourt, Brace, Jovanovich, New York (second ed., Academic Press, New York, 1974, third ed., 2001)
    • (1968) A Course in Probability Theory
    • Chung, K.-L.1
  • 12
    • 0348165618 scopus 로고
    • Sur l'ensemble des puissances d'une loi de probabilité
    • Doeblin W. Sur l'ensemble des puissances d'une loi de probabilité. Studia Math. 9 (1940) 71-96
    • (1940) Studia Math. , vol.9 , pp. 71-96
    • Doeblin, W.1
  • 13
    • 33750963101 scopus 로고
    • A necessary and sufficient condition for the validity of the weak law of large numbers
    • Ehrenfeucht A., and Fisz M. A necessary and sufficient condition for the validity of the weak law of large numbers. Bull. Acad. Pol. Sci. 9 (1960) 17-19
    • (1960) Bull. Acad. Pol. Sci. , vol.9 , pp. 17-19
    • Ehrenfeucht, A.1    Fisz, M.2
  • 15
    • 34250943556 scopus 로고
    • Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung
    • Feller W. Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung. Math. Z. 40 (1935) 521-559
    • (1935) Math. Z. , vol.40 , pp. 521-559
    • Feller, W.1
  • 16
    • 33750939660 scopus 로고    scopus 로고
    • W. Feller, An Introduction to Probability Theory and its Applications, third ed., vol. I, Wiley, 1968 (first ed., 1950, second ed., 1957).
  • 17
    • 33750963313 scopus 로고    scopus 로고
    • W. Feller, An Introduction to Probability Theory and its Applications, second ed., vol. II, Wiley, 1971 (first ed., 1966).
  • 18
    • 84958156266 scopus 로고
    • Limiting forms of the frequency distribution of the largest or smallest member of a sample
    • (reprinted in R.A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, and in: J.H. Bennett (Ed.), Collected Papers of R.A. Fisher, vol. II, pp. 1925-1931, The University of Adelaide, 1972, pp. 208-219)
    • Fisher R.A., and Tippett L.H.C. Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Cambridge Phil. Soc. 24 (1928) 180-190 (reprinted in R.A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, and in: J.H. Bennett (Ed.), Collected Papers of R.A. Fisher, vol. II, pp. 1925-1931, The University of Adelaide, 1972, pp. 208-219)
    • (1928) Proc. Cambridge Phil. Soc. , vol.24 , pp. 180-190
    • Fisher, R.A.1    Tippett, L.H.C.2
  • 19
    • 0002689711 scopus 로고
    • Sur la loi de probabilité de l'écart maximum
    • Fréchet M. Sur la loi de probabilité de l'écart maximum. Ann. Soc. Math. Polon. 6 (1937) 93-116
    • (1937) Ann. Soc. Math. Polon. , vol.6 , pp. 93-116
    • Fréchet, M.1
  • 21
    • 33750932185 scopus 로고
    • On the theory of domains of attraction for stable laws (Russian)
    • Gnedenko B.V. On the theory of domains of attraction for stable laws (Russian). Gos. Univ. Uch. Zap. Mat. 30 3 (1939) 61-81
    • (1939) Gos. Univ. Uch. Zap. Mat. , vol.30 , Issue.3 , pp. 61-81
    • Gnedenko, B.V.1
  • 22
    • 0000005110 scopus 로고
    • Sur la distribution limite du terme maximum d'une série aléatoire
    • Gnedenko B.V. Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44 (1943) 423-453
    • (1943) Ann. Math. , vol.44 , pp. 423-453
    • Gnedenko, B.V.1
  • 25
    • 0003040223 scopus 로고
    • Fighting the arch-enemy with mathematics
    • de Haan L. Fighting the arch-enemy with mathematics. Stat. Neerl. 44 (1990) 45-68
    • (1990) Stat. Neerl. , vol.44 , pp. 45-68
    • de Haan, L.1
  • 26
    • 33750941961 scopus 로고    scopus 로고
    • 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).
  • 27
    • 0002478697 scopus 로고
    • Sur un mode de croissance régulière des fonctions
    • Karamata J. Sur un mode de croissance régulière des fonctions. Mathematica (Cluj) 4 (1930) 38-53
    • (1930) Mathematica (Cluj) , vol.4 , pp. 38-53
    • Karamata, J.1
  • 28
    • 0002028669 scopus 로고
    • Neuer Beweis und Verallgemeinerung der Tauberschen Sätze, welche die Laplacessche und Stieltjessche Transformationen betreffen
    • Karamata J. Neuer Beweis und Verallgemeinerung der Tauberschen Sätze, welche die Laplacessche und Stieltjessche Transformationen betreffen. J. Reine Angew. Math. 164 (1931) 27-39
    • (1931) J. Reine Angew. Math. , vol.164 , pp. 27-39
    • Karamata, J.1
  • 29
    • 0041806809 scopus 로고
    • Sul dominio di attrazione della legge di Gauss
    • Khintchine A.Ya. Sul dominio di attrazione della legge di Gauss. G. Ist. Ital. Attuari 6 (1935) 371-393
    • (1935) G. Ist. Ital. Attuari , vol.6 , pp. 371-393
    • Khintchine, A.Ya.1
  • 31
    • 33750949975 scopus 로고    scopus 로고
    • E. Landau, Sur les valeurs moyennes de certaines fonctions arithmétiques, Bull. Acad. R. Belgique (1911) 443-472.
  • 33
    • 0042549874 scopus 로고
    • Propriétés asymptotiques des sommes des variables aléatoires indépendantes ou enchainées
    • Lévy P. Propriétés asymptotiques des sommes des variables aléatoires indépendantes ou enchainées. J. Math. Pures Appl. 14 8 (1935) 347-402
    • (1935) J. Math. Pures Appl. , vol.14 , Issue.8 , pp. 347-402
    • Lévy, P.1
  • 35
    • 0009029434 scopus 로고
    • Relative stability and the strong law of large numbers
    • Maller R.A. Relative stability and the strong law of large numbers. Z. Wahrschein. 43 (1978) 141-148
    • (1978) Z. Wahrschein. , vol.43 , pp. 141-148
    • Maller, R.A.1
  • 36
    • 0042342292 scopus 로고
    • Relative stability, characteristic functions and stochastic compactness
    • Maller R.A. Relative stability, characteristic functions and stochastic compactness. J. Austr. Math. Soc. A 28 (1979) 499-509
    • (1979) J. Austr. Math. Soc. A , vol.28 , pp. 499-509
    • Maller, R.A.1
  • 40
    • 33750950490 scopus 로고    scopus 로고
    • G. Pólya, Über eine neue Weise, bestimmte Integrale in der analytischen Zahlentheorie zu gebrauchen, Göttinger Nachr. (1917) 149-159.
  • 43
    • 0009939154 scopus 로고
    • Relatively stable random walks
    • Rogozin B.A. Relatively stable random walks. Theory Probab. Its. Appl. 16 (1976) 575-595
    • (1976) Theory Probab. Its. Appl. , vol.16 , pp. 575-595
    • Rogozin, B.A.1
  • 44
    • 33750940812 scopus 로고
    • A single form for the conditions for attraction to stable laws
    • Sakovich G.N. A single form for the conditions for attraction to stable laws. Theory Prob. Its Appl. 1 (1956) 322-325
    • (1956) Theory Prob. Its Appl. , vol.1 , pp. 322-325
    • Sakovich, G.N.1
  • 45
    • 0002175302 scopus 로고
    • Functional equations and the Galton-Watson process
    • Seneta E. Functional equations and the Galton-Watson process. Advances Appl. Probab. 1 (1969) 1-42
    • (1969) Advances Appl. Probab. , vol.1 , pp. 1-42
    • Seneta, E.1
  • 46
    • 0016103640 scopus 로고
    • Regularly varying functions in the theory of simple branching processes
    • Seneta E. Regularly varying functions in the theory of simple branching processes. Advances Appl. Probab. 6 (1974) 408-420
    • (1974) Advances Appl. Probab. , vol.6 , pp. 408-420
    • Seneta, E.1
  • 48
    • 33750932791 scopus 로고
    • Karamata's iteration theory and normed regularly varying sequences in a historical light
    • Seneta E. Karamata's iteration theory and normed regularly varying sequences in a historical light. Publ. Inst. Math. Beograd 48 62 (1990) 45-51
    • (1990) Publ. Inst. Math. Beograd , vol.48 , Issue.62 , pp. 45-51
    • Seneta, E.1
  • 49
    • 33750965586 scopus 로고    scopus 로고
    • Karamata's characterization theorem, Feller, and regular variation in probability theory
    • Seneta E. Karamata's characterization theorem, Feller, and regular variation in probability theory. Publ. Inst. Math. Beograd 71 85 (2002) 79-89
    • (2002) Publ. Inst. Math. Beograd , vol.71 , Issue.85 , pp. 79-89
    • Seneta, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.