On Max-Multiscaling Distributions as Extended Max-Semistable Ones

References

• Balkema , A.A. and Resnick , S.I. 1977 . Max-infinite divisibility . J. Appl. Prob. , 14 : 309 – 319 .
   Web of Science ®Google Scholar
• Crump , K. and Mode , C.J. A general age-dependent branching processes . J. Math. Anal. Appl. , 1968 and 1969, Parts I and II, 24, 494–508 and 25, 8–17
   Google Scholar
• Embrechts , P. , Klüppelberg , C. and Mikosch , T. 1997 . Modelling Extremal Events , Applications of Mathematics 33 Springer-Verlag .
   Google Scholar
• Guivarc'h , Y. 1990 . Sur une extension de la notion de loi semistable . Ann. Inst. H. Poincaré, Probabilitiés et Statistiques , 26 : 261 – 285 .
   Web of Science ®Google Scholar
• Grinevich , I.V. 1992 . Max-semistable limit laws under linear and power normalization . Theory Probab. Appl. , 37 : 720 – 721 .
   Google Scholar
• Grinevich , I.V. 1993 . “ Max-semistable laws under linear and power normalization ” . In Stability Problems for Stochastic Models 65 – 73 . Perm : TVP/VSP/Moscow/Utrecht .
   Google Scholar
• Grinevich , I.V. 1993 . Domains of attraction of the max-semistable laws under linear and power normalization . Theory Probab. Appl. , 38 : 640 – 650 .
   Google Scholar
• Huillet , T. , Porzio , A. and Ben Alaya , M. 2000 . On the physical relevance of max and log-max selfsimilar distributions . Eur. Phys. J. B , 17 ( 1 ) : 147 – 158 . [CROSSREF]
   Google Scholar
• Kahane , J.P. and Peyriére , J. 1976 . Sur certaines martingales de Benoit Mandelbrot . Adv. Math. , 22 : 131 – 345 . [CROSSREF]
   Web of Science ®Google Scholar
• Becker-Kern , P. 2001 . Max-semistable hemigroups: Structure, domains of attraction and limit theorems with random sample size . Probab. Math. Statist. , 21 ( 2 ) : 441 – 465 .
   Google Scholar
• Liu , Q. 1997 . Sur une équation fonctionnelle et ses applications: Une extension du théorème de Kesten-Stigum concernant des processus de branchement . Adv. Appl. Prob. , 29 : 353 – 373 .
   Google Scholar
• Lukacs , E. 1983 . Developments in Characteristic Function Theory London and High Wycombe : C. Griffin and Co. Ltd .
   Google Scholar
• Mandelbrot , B.B. 1974 . Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire: (quelques extensions) . C.R.A.S. Pairs , 278 : 289 – 292 . and 355–358. Parts I and II
   Google Scholar
• Mejzler , D. 1965 . On a certain class of limit distributions and their domain of attraction . Trans. Am. Math. Soc. , 117 : 205 – 236 .
   Google Scholar
• Mohan , N.R. and Ravi , S. 1992 . Max-domains of attraction of univariate and multivariate p-max-stable laws . Theory Probab. Appl. , 37 : 632 – 643 .
   Web of Science ®Google Scholar
• Megyesi , Z. 2002 . Domains of geometric partial attraction of max-semistable laws: Structure, merge and almost sure limit theorems . J. Theor. Probab. , 15 ( 4 ) : 973 – 1005 . [CROSSREF]
   Google Scholar
• Pancheva , E. 1995 . Max-semistable laws . J. Math. Sci. , 76 : 2177 – 2180 .
   Google Scholar
• Pancheva , E. 1998 . Self-similar extremal processes . J. Math. Sci. , 92 ( 3 ) : 3911 – 3920 .
   Google Scholar
• Pancheva , E. 2000 . Semi-selfsimilar extremal processes . J. Math. Sci. , 99 ( 3 ) : 1306 – 1316 .
   Google Scholar
• Rao , C.R. and Shanbhag , D.N. 1994 . Choquet-Deny Type Functional Equations with Applications to Stochastic Models , Wiley Series in Probability and Mathematical Statistics Chichester : John Wiley and Sons, Ltd .
   Google Scholar
• Ravi , S. 1991 . Tail equivalence of distribution functions belonging to the max domains of attraction of univariate p-max stable laws . J. Indian Stat. Assoc. , 29 : 69 – 77 .
   Google Scholar
• Ravi , S. 2000 . Limit laws for power normalized partial maxima of independent random variables having one of m specified distributions . Calcutta Stat. Assoc. Bull. , 50 ( 197–198 ) : 1 – 15 .
   Google Scholar
• Resnick , S.I. 1987 . Extreme Value Distributions, Regular Variations and Point Processes New York : Springer-Verlag .
   Google Scholar
• Resnick , S.I. and Rubinovitch , M. 1973 . The structure of extremal processes . Ann. Appl. Prob. , 5 : 287 – 307 .
   Google Scholar
• Sato , Ken-iti. 1999 . Lévy Processes and Infinitely Divisible Distributions , Cambridge Studies in Advanced Mathematics, 68 Cambridge : Cambridge University Press .
   Google Scholar
• Sornette , D. 1998 . Discrete scale invariance and complex dimensions . Phys. Rep. , 297 : 239 – 270 . [CROSSREF]
   Web of Science ®Google Scholar