Limit theorems for random sets: An application of probability in banach space results (original) (raw)
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- Araujo, A. and Giné, E. (1980). The central limit theorem for real and Banach valued random variables. Wiley, New York.
MATH Google Scholar - Arrow, K.J. and Hahn, F.H. (1971). General Competitive Analysis. Holden-Day, San Francisco.
MATH Google Scholar - Artstein, Z. and Vitale, R.A. (1975). A strong law of large numbers for random compact sets. Ann. Prob. 3, 879–882.
Article MathSciNet MATH Google Scholar - Aumann, R.J. (1965). Integrals of set-valued functions. Indiana Math. J. 24, 433–441.
MathSciNet MATH Google Scholar - Billingsley, P. (1968). Convergence of probability measures. Wiley, New York.
MATH Google Scholar - Byrne, C.L. (1978). Remarks on the set-valued integrals of Debreu and Aumann. J. Math. Analysis and Appl. 62, 243–246.
Article MathSciNet MATH Google Scholar - Cressie, N. (1978). A strong limit theorem for random sets. Adv. Appl. Prob. Suppl. 10, 36–46.
Article MathSciNet MATH Google Scholar - Cressie, N. (1979). A central limit theorem for random sets. Z. Wahrscheinlichkeitstheorie 49, 37–47.
Article MathSciNet MATH Google Scholar - Debreu, G. (1966). Integration of correspondences. Proc. Fifth Berkeley Symp. Math. Statist. and Probability 2, 351–372. Univ. of California Press.
MathSciNet Google Scholar - Garling, D.J.H. and Gordon, Y. (1971). Relations between some constants associated with finite dimensional Banach spaces. Israel J. Math. 9, 346–361.
Article MathSciNet MATH Google Scholar - Giné, E. (1976). Bounds for the speed of convergence in the central limit theorem in C(S). Z. Wahrscheinlichkeitstheorie 36, 317–331.
Article MathSciNet MATH Google Scholar - Giné, E. (1980). Sums of independent random variable and sums of their squares. Pub. Mat. UAB No 22, Actes VII JMHL.
Google Scholar - Giné, E. and Marcus, M.B. (1981). On the central limit theorem in C(K). In "Aspects statistiques et aspects physiques des processus Gaussiens", 361–383. Colloques Intern of the CNRS no 307, CNRS, Paris.
Google Scholar - Hormander, L. (1954). Sur la fonction d'appui des ensembles convexes dans un espace localement convexe. Arkiv för Matematik 3, 181–186.
Article MathSciNet MATH Google Scholar - Jain, N.C. and Marcus, M.B. (1975). Central limit theorem for C(S)-valued random variables. J. Funct. Anal. 19, 216–231.
Article MathSciNet MATH Google Scholar - Kendall, D.G. (1974). Foundations of a theory of random sets. In Stochastic Geometry, ed. E.F. Harding and D.G. Kendall, Wiley, New York.
Google Scholar - Kuratowski, K. and Ryll-Nardzewski, C. (1965). A general theory of selectors. Bull. Pol. Acad. Sci. 13, 397–403.
MathSciNet MATH Google Scholar - Lindenstrauss, J. and Tzafriri, L. (1979). Classical Banach Spaces, Vol. II: Function Spaces. Springer-Verlag, New York.
Book MATH Google Scholar - Matheron, G. (1975). Random Sets and Integral Geometry. Wiley, New York.
MATH Google Scholar - Mityagin, B.S. (1961). Approximate dimension and bases in nuclear spaces. Russian Math. Surveys 16, 59–127.
Article MathSciNet MATH Google Scholar - Mourier, E. (1955). L-random elements and L*-random elements in Banach spaces. Proc. Third Berkeley Symp. Math. Statist. and Probability 2, 231–242. Univ. of California Press.
MathSciNet Google Scholar - Pisier, G. (1975). Le Théorème de la limite centrale et la loi due logarithme itéré dans les espace de Banach. Séminaire Maurey-Schwartz 1975–76, Exposés 3 et Ecole Polytechnique, Paris.
Google Scholar - Pisier, G. (1979). Some applications of the complex interpolation method to Banach lattices. Journal d'Analyse Math. 35, 264–281.
Article MathSciNet MATH Google Scholar - Pisier, G. and Zinn, J. (1978). On the limit theorems for random variables with values in the spaces Lp, p ≥ 2. Z. Wahrscheinlichkeitstheorie 41, 289–304.
Article MathSciNet MATH Google Scholar - Puri, M.L. and Ralescu, D.A. (1982). Strong law of large numbers for Banach space valued random sets. To appear in Ann. Probability, February, 1983.
Google Scholar - Robbins, H.E. (1944). On the measure of a random set. Ann. Math. Statist. 14, 70–74.
Article MathSciNet MATH Google Scholar - Robbins, H.E. (1945). On the measure of a random set, II. Ann. Math. Statist. 15, 342–347.
Article MathSciNet MATH Google Scholar - Rvačeva, E.L. (1962). On domains of attraction of multidimensional distributions. Selected Translations in Math. Stat. and Probability v. 1, 183–205.
Google Scholar - Trader, D.A. and Eddy, W.F. (1981). A central limit theorem for Minkowski sums of random sets. Carnegie-Mellon University Technical Report No. 228.
Google Scholar - Vitale, R.A. (1981). A central limit theorem for random convex sets. Technical Report Claremont Graduate School.
Google Scholar - Weil, W. (1982). An application of the central limit theorem for Banach space-valued random variables to the theory of random sets. Z. Wahrscheinlichkeitstheorie 60, 203–208.
Article MathSciNet MATH Google Scholar
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Authors and Affiliations
- Department of Mathematics, Louisiana State University, 70803, Baton Rouge, LA
Evarist Giné - Department of Mathematics, Texas, A & M
Evarist Giné - Department of Mathematics, Tufts University, 02155, Medford, MA
Marjorie G. Hahn - Department of Mathematics, Texas A &M, 77843, College Station, TX
Joel Zinn
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- Evarist Giné
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Anatole Beck Konrad Jacobs
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Giné, E., Hahn, M.G., Zinn, J. (1983). Limit theorems for random sets: An application of probability in banach space results. In: Beck, A., Jacobs, K. (eds) Probability in Banach Spaces IV. Lecture Notes in Mathematics, vol 990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064267
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- DOI: https://doi.org/10.1007/BFb0064267
- Published: 25 August 2006
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