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

• Autorzy: G. Krupa
• 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].

Słowa kluczowe

EN

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

Kategorie tematyczne

• 47A35: Ergodic theory
• 26B20: Integral formulas (Stokes, Gauss, Green, etc.)
• 28D99: None of the above, but in this section
• 26E25: Set-valued functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 131
• Numer: 3
• Strony: 289-302

Daty

wydano

1998

otrzymano

1997-10-13

Twórcy

autor

G. Krupa

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

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.