Multifunctions of faces for conditional expectations of selectors and Jensen's inequality

A. Kozek and Z. Suchanecki

Journal of Multivariate Analysis, 1980, vol. 10, issue 4, 579-598

Abstract: Let (T, , P) be a probability space, a P-complete sub-[delta]-algebra of and X a Banach space. Let multifunction t --> [Gamma](t), t [set membership, variant] T, have a [circle times operator] (X)-measurable graph and closed convex subsets of X for values. If x(t) [epsilon] [Gamma](t) P-a.e. and y(·) [epsilon] Ep x(·), then y(t) [epsilon] [Gamma](t) P-a.e. Conversely, x(t) [epsilon] F([Gamma](t), y(t)) P-a.e., where F([Gamma](t), y(t)) is the face of point y(t) in [Gamma](t). If X = , then the same holds true if [Gamma](t) is Borel and convex, only. These results imply, in particular, extensions of Jensen's inequality for conditional expectations of random convex functions and provide a complete characterization of the cases when the equality holds in the extended Jensen inequality.

Keywords: Multifunction; random; convex; set; face; of; a; convex; set; conditional; expectation; selector; Jensen's; inequality (search for similar items in EconPapers)
Date: 1980
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(80)90071-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:10:y:1980:i:4:p:579-598

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().