Download PDF - Ergodic theorems for subadditive superstationary families of random sets with values in Banach spacesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces

Authors 1

Affiliations

  1. Mathematical Institute, University of Utrecht, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands

Abstract

Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in ℝd are considered. Techniques used here are inspired by [3].

Keywords

ENG
multivalued ergodic theorems, measurable multifunctions, random sets, subadditive superstationary processes, set convergence

Bibliography

  1. M. Abid, Un théorème ergodique pour des processus sous-additifs et sur-stationnaires, C. R. Acad. Sci. Paris Sér. A 287 (1978), 149-152.
  2. Z. Artstein and J. C. Hansen, Convexification in limit laws of random sets in Banach spaces, Ann. Probab. 13 (1985), 307-309.
  3. E. J. Balder and Ch. Hess, Two generalizations of Komlós' theorem with lower closure-type applications, J. Convex Anal. 3 (1996), 25-44.
  4. J. Brooks and R. V. Chacon, Continuity and compactness of measures, Adv. Math. 37 (1980), 16-26.
  5. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977.
  6. A. Costé, La propriété de Radon-Nikodym en intégration multivoque, C. R. Acad. Sci. Paris Sér. A 280 (1975), 1515-1518.
  7. A. Costé, Contribution à la théorie de l'intégration multivoque, thèse d'état, Université Pierre et Marie Curie, Paris, 1977.
  8. J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1979.
  9. J. M. Hammersley, Postulates for subadditive processes, Ann. Probab. 2 (1974), 652-680.
  10. Ch. Hess, On multivalued martingales whose values may be unbounded: Martingale selectors and Mosco convergence, J. Multivariate Anal. 39 (1991), 175-201.
  11. F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multivalued functions, ibid. 7 (1977), 149-182.
  12. J. F. C. Kingman, The ergodic theory of subadditive stochastic processes, J. Roy. Statist. Soc. Ser. B 30 (1968), 499-510.
  13. U. Krengel, Un théorème ergodique pour les processus sur-stationnaires, C. R. Acad. Sci. Paris Sér. A 282 (1976), 1019-1021.
  14. K. Schürger, Ergodic theorems for subadditive superstationary families of convex compact random sets, Z. Wahrsch. Verw. Gebiete 62 (1983), 125-135.
  15. F. A. Valentine, Convex Sets, McGraw-Hill and Wiley, New York, 1968.
Studia Mathematica
1998/131/3
Export to PBN, Opens in new tab
Pages:
289-302
Main language of publication
English
Received
1997-10-13
Published
1998
Exact and natural sciences