Tytuł artykułu
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Warianty tytułu
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Abstrakty
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
Czasopismo
Rocznik
Tom
Strony
125--146
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Mathematics University of Nevada Reno NV 89557 USA
autor
- 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.
- [2] Billingsley, P., Convergence of types in k-space, Z. Wahrsch. verw. Geb. 5 (1966), 175-179.
- [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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