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M-infinitely divisible random compact convex sets

Part of the Lecture Notes in Mathematics book series (LNM,volume 1153)

Keywords

  • Banach Space
  • Central Limit Theorem
  • Compact Convex
  • Steiner Point
  • Separable Banach Space

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References

  1. Araujo, A. and Giné, E. (1980). The central limit theorem for real and Banach valued random variables. Wiley, New York.

    MATH  Google Scholar 

  2. Artstein, Z. (1984). Limit laws for multifunctions applied to an optimization problem. Preprint.

    Google Scholar 

  3. Artstein, Z. and Hart, S. (1981). Law of large numbers for random sets and allocation processes. Math. Operations Res. 6, 485–492.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Artstein, Z. and Vitale, R. A. (1975). A strong law of large numbers for random compact sets. Ann. Prob. 3, 879–882.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Byrne, C. L. (1978). Remarks on the set-valued integrals of Debreu and Aumann. J. Math. Analysis and Appl. 62, 243–246.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Cressie, N. (1979). A central limit theorem for random sets. Z. Wahrscheinlichkeitstheorie 49, 37–47.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Debreu, G. (1966). Integration of correspondences. Proc. Fifth Berkeley Symp. Math. Statist. and Probability 2, 351–372. Univ. of California Press.

    Google Scholar 

  8. Dunford, N. and Schwartz, J. T. (1958). Linear Operators. Part I. Interscience Publishers, Inc. N.Y.

    MATH  Google Scholar 

  9. Dvoretzsky, A. (1961). Some results on convex bodies and Banach spaces, Proc. Symp. on Linear Spaces, 123–160. Jerusalem.

    Google Scholar 

  10. Garling, D.J.H. and Gordon, Y. (1971). Relations between some constants associated with finite dimensional Banach spaces. Israel J. Math. 9, 346–361.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Giné, E. and Hahn, M. G. (1984). Characterization and domains of attraction of p-stable random compact convex sets. Ann. Probability 14.

    Google Scholar 

  12. Giné, E. and Hahn, M. G. (1984). The Lévy-Khinchin representation for random compact convex subsets which are infinitely divisible under Minkowski addition. To appear in Z. Wahrscheinlichkeitstheorie.

    Google Scholar 

  13. Giné, E.; Hahn, M. G and Zinn, J. (1983). Limit theorems for random sets: an application of probability in Banach space results. Lect. Notes in Math. 990, 112–135.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Hormander, L. (1954). Sur la fonction d’appui des convexes dans un espace localement convexe. Arkiv. för Matematik 3, 181–186.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Lindenstrauss, J. (1964). On nonlinear projections in Banach spaces. Michigan Mathematical Journal 11, 263–287.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Lyashenko, N. N. (1982). Limit theorems for sums of independent compact random subsets of Euclidean space. J. Soviet Math. 20, 2187–2196.

    CrossRef  MATH  Google Scholar 

  17. Lyashenko, N. N. (1983). Statistics of random compacts in Euclidean space. J. Soviet Math. 21, 76–92.

    CrossRef  MATH  Google Scholar 

  18. Mase, S. (1979). Random convex sets which are infinitely divisible with respect to Minkowski addition. Adv. Appl. Prob. 11, 834–850.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Tortrat, A. (1977). Sur le support des lois indéfiniment divisibles dans les espaces vectoriels localement convexes. Ann. Inst. Henri Poincaré 13, 27–43.

    MathSciNet  MATH  Google Scholar 

  20. Trader, D. A. (1981) Infinitely divisible random sets. Thesis, Carnegie-Mellon University.

    Google Scholar 

  21. Trader, D. A. and Eddy, W. F. (1981). A central limit theorem for Minkowski sums of random sets. Technical Report No. 228, Carnegie-Mellon University.

    Google Scholar 

  22. Vitale, R. A. (1981). A central limit theorem for random convex sets. Technical report, Claremont Graduate School.

    Google Scholar 

  23. Vitale, R. A. (1983). On Gaussian random sets. To appear in Proceedings of the conference on stochastic geometry, geometric statistics, and stereology. Oberwolfach. (R. V. Ambartzumian and W. Weil eds.) Teubner-Verlag 222–224.

    Google Scholar 

  24. 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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1985 Springer-Verlag

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Giné, E., Hahn, M.G. (1985). M-infinitely divisible random compact convex sets. In: Beck, A., Dudley, R., Hahn, M., Kuelbs, J., Marcus, M. (eds) Probability in Banach Spaces V. Lecture Notes in Mathematics, vol 1153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074952

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  • DOI: https://doi.org/10.1007/BFb0074952

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