PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1998 | 131 | 3 | 289-302
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $ℝ^d$ are considered. Techniques used here are inspired by [3].
Twórcy
autor
  • Mathematical Institute, University of Utrecht, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands, krupa@math.ruu.nl
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv131i3p289bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.