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Multivariable regular variation of functions and measures

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Regular variation is an asymptotic property of functions and measures. The one variable theory is well-established, and has found numerous applications in both pure and applied mathematics. In this paper we present several new results on mul-tivariable regular variation for functions and measures.
Wydawca
Rocznik
Strony
125--146
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Department of Mathematics University of Nevada Reno NV 89557 USA
  • Department of Mathematics University of Dortmund 44221 Dortmund Germany
Bibliografia
  • [1] Balkema, A.A., Monotone Transformations and Limit Laws, Mathematical Centre Tracts 45, Mathematisch Centrum, Amsterdam, 1973.
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  • [3] Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968.
  • [4] Bingham, N., Goldie, C. and Teugels, J., Regular Variation, Encyclopedia of Mathematics and its Applications 27, Cambridge University Press, Cambridge, 1987.
  • [5] Curtis, C., Linear Algebra, 3rd ed., Allyn and Bacon, Boston, 1974.
  • [6] Feller, W., An Introduction to Probability Theory and Its Applications, Vol. II, 2nd Ed., Wiley, New York, 1971.
  • [7] Fisz, M., A generalization of a theorem of Khintchin, Studia Math. 14 (1954), 310-313.
  • [8] de Haan, L., Omey, E. and Resnick, S., Domains of attraction and regular variation in Rd, J. Multivatiate Anal. 14 (1984), 17-33.
  • [9] Hirsch, M. and Smale, S., Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York, 1974 .
  • [10] Holmes, J., Hudson, W. and Mason, J.D., Operator stable laws: multiple exponents and elliptical symmetry, Ann. Probab. 10 (1982), 602-612.
  • [11] Hudson, W., Jurek, Z. and Veeh, J., The symmetry group and exponents of operator stable probability measures Ann. Probab. 14 (1986), 1014-1023.
  • [12] Jakimiv, A.L., Many-dimensional Tauberian Theorems and their application to Bellman-Harris branching processes (in Russian), Math. Sbornik 115(157) (1981), 463-477.
  • [13] Jurek, Z.J., Polar coordinates in Banach spaces, Bull. Acad. Pol. Math. 32 (1984), 61-66.
  • [14] Meerschaert, M., Regular variation in Rfc, Proc. Amer. Math. Soc. 102 (1988), 341-348.
  • [15] Meerschaert, M., Spectral decomposition for generalized domains of attraction, Ann. Probab. 19 (1991), 875-892.
  • [16] Meerschaert, M., Norming operators for generalized domains of attraction, J. Theoret. Probab. 7 (1994), 793-798.
  • [17] Meerschaert, M. and Scheffler, H.-P., Spectral decomposition for generalized domains of semistable attraction, J. Theoret. Probab. 10 (1997), 51-71.
  • [18] Scheffler, H.-P., Multivariable R-0 variation and generalized domains of semistable attraction, Habilitation Thesis, University of Dortmund, 1997.
  • [19] Samorodnitsky, G. and Taqqu, M.S., Stable non-Gaussian Random Processes, Chapman and Hall, New York, 1994.
  • [20] Seneta, E., Regularly Varying Functions, Lecture Notes in Math. 508, Springer, Berlin, 1976.
  • [21] Sharpe, M., Operator-stable probability distributions on vector groups, Trans. Amer. Math. Soc. 136 (1969), 51-65.
  • [22] Siam, A., Regular Variation in and the Abel-Tauber Theorem, Technical Report T. W. 189, Mathematisch Instituut Rijksuniversiteit Groningen, The Netherlands, 1977.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0012-0034
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