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 are considered. Techniques used here are inspired by [3].
@article{bwmeta1.element.bwnjournal-article-smv131i3p289bwm,
author = {G. Krupa},
title = {Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {289-302},
zbl = {0921.28008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv131i3p289bwm}
}
Krupa, G. Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces. Studia Mathematica, Tome 129 (1998) pp. 289-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv131i3p289bwm/
[00000] [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. | Zbl 0386.60028
[00001] [2] Z. Artstein and J. C. Hansen, Convexification in limit laws of random sets in Banach spaces, Ann. Probab. 13 (1985), 307-309. | Zbl 0554.60022
[00002] [3] E. J. Balder and Ch. Hess, Two generalizations of Komlós' theorem with lower closure-type applications, J. Convex Anal. 3 (1996), 25-44.
[00003] [4] J. Brooks and R. V. Chacon, Continuity and compactness of measures, Adv. Math. 37 (1980), 16-26. | Zbl 0463.28003
[00004] [5] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977.
[00005] [6] A. Costé, La propriété de Radon-Nikodym en intégration multivoque, C. R. Acad. Sci. Paris Sér. A 280 (1975), 1515-1518. | Zbl 0313.28007
[00006] [7] A. Costé, Contribution à la théorie de l'intégration multivoque, thèse d'état, Université Pierre et Marie Curie, Paris, 1977.
[00007] [8] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1979.
[00008] [9] J. M. Hammersley, Postulates for subadditive processes, Ann. Probab. 2 (1974), 652-680. | Zbl 0303.60044
[00009] [10] Ch. Hess, On multivalued martingales whose values may be unbounded: Martingale selectors and Mosco convergence, J. Multivariate Anal. 39 (1991), 175-201. | Zbl 0746.60051
[00010] [11] F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multivalued functions, ibid. 7 (1977), 149-182. | Zbl 0368.60006
[00011] [12] J. F. C. Kingman, The ergodic theory of subadditive stochastic processes, J. Roy. Statist. Soc. Ser. B 30 (1968), 499-510. | Zbl 0182.22802
[00012] [13] U. Krengel, Un théorème ergodique pour les processus sur-stationnaires, C. R. Acad. Sci. Paris Sér. A 282 (1976), 1019-1021. | Zbl 0343.60017
[00013] [14] K. Schürger, Ergodic theorems for subadditive superstationary families of convex compact random sets, Z. Wahrsch. Verw. Gebiete 62 (1983), 125-135. | Zbl 0489.60005
[00014] [15] F. A. Valentine, Convex Sets, McGraw-Hill and Wiley, New York, 1968.