Convergence of conditional expectations for unbounded closed convex random sets
Castaing, Charles ; Ezzaki, Fatima ; Hess, Christian
Studia Mathematica, Tome 122 (1997), p. 133-148 / Harvested from The Polish Digital Mathematics Library

We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form EnXn where (n) is a decreasing sequence of sub-σ-algebras and (Xn) is a sequence of closed convex random sets in a separable Banach space.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216402
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     author = {Charles Castaing and Fatima Ezzaki and Christian Hess},
     title = {Convergence of conditional expectations for unbounded closed convex random sets},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {133-148},
     zbl = {0902.60003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv124i2p133bwm}
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Castaing, Charles; Ezzaki, Fatima; Hess, Christian. Convergence of conditional expectations for unbounded closed convex random sets. Studia Mathematica, Tome 122 (1997) pp. 133-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv124i2p133bwm/

[00000] [A] H. Attouch, Variational Convergence for Functions and Operators, Appl. Math. Ser., Pitman, Boston, 1984. | Zbl 0561.49012

[00001] [CE1] C. Castaing and F. Ezzaki, Variational inequalities for integrand martingales and additive random sequences, Acta Math. Vietnam. 18 (1993), 137-171. | Zbl 0886.60023

[00002] [CE2] C. Castaing and F. Ezzaki, SLLN for convex random sets and random lower semicontinuous integrands, preprint, Département de Mathématiques, Université Montpellier II, 1995. | Zbl 0905.60019

[00003] [CV] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, 1977. | Zbl 0346.46038

[00004] [Ch] A. Choukairi-Dini, Contribution à l'étude des martingales et au lemme de Fatou multivoque, Thèse, Université Montpellier II, 1988.

[00005] [Co] J. Couvreux, Etude de problèmes de convergence et d'approximation de fonctionnelles intégrales et d'espérances conditionnelles multivoques, Thèse, Université Paris-Dauphine, 1995.

[00006] [Ez1] F. Ezzaki, Contributions aux problèmes de convergence des suites adaptées et des ensembles aléatoires, Thèse, Université Montpellier II, 1993.

[00007] [Ez2] F. Ezzaki, A general dominated convergence theorem for unbounded random sets, Bull. Polish Acad. Sci. Math. 44 (1996), 353-361. | Zbl 0879.60049

[00008] [He1] C. Hess, Lemme de Fatou et convergence dominée pour les ensembles aléatoires non bornés et des intégrandes, Sém. Analyse Convexe Montpellier, exp. no. 8, 1986.

[00009] [He2] C. Hess, Convergence of conditional expectations for unbounded random sets, integrands, and integral functionals, Math. Oper. Res. 16 (1991), 627-649. | Zbl 0744.28010

[00010] [He3] C. Hess, Mesurabilité, convergence et approximation des multifonctions à valeurs dans un e.l.c.s., Sém. Analyse Convexe Montpellier, exp. no. 9, 1985.

[00011] [He4] C. Hess, Measurability and integrability of the weak upper limit of a sequence of multifunctions, J. Math. Anal. Appl. 153 (1990), 226-229. | Zbl 0748.47046

[00012] [He5] C. Hess, Multivalued strong law of large numbers in the slice topology. Application to integrands, Set-Valued Anal. 2 (1994), 183-205.

[00013] [Hi1] F. Hiai, Multivalued conditional expectations, multivalued Radon-Nikodym theorems, integral representation of additive operators and multivalued strong laws of large numbers, preprint, Conference of Catania, 1983.

[00014] [Hi2] F. Hiai, Convergence of conditional expectations and strong laws of large numbers for multivalued random variables, Trans. Amer. Math. Soc. 291 (1985), 613-627. | Zbl 0583.60007

[00015] [HU] F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multivalued functions, J. Multivariate Anal. 7 (1977), 149-182. | Zbl 0368.60006

[00016] [Mo] U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Adv. in Math. 3 (1969), 151-155.

[00017] [Ne] J. Neveu, Martingales à temps discret, Masson, 1972.

[00018] [SZ] D. Szynal and W. Zięba, On some characterization of almost sure convergence, Bull. Polish Acad. Sci. Math. 34 (1986), 635-642. | Zbl 0615.60027

[00019] [We] R. Wets, Convergence of convex functions, variational inequalities and convex optimization problems, in: Variational Inequalities and Complementarity Problems, R. W. Cottle, F. Giannessi, and J. L. Lions (eds.), Wiley, Chichester, 1980, 375-403.

[00020] [Zi] W. Zięba, On the L1 convergence of conditional amarts, J. Multivariate Anal. 26 (1988), 104-110. | Zbl 0649.60040