The purpose of this paper is to prove some convergence theorems of
closed and convex set valued sub- and supermartingales in the
Kuratowski–Mosco sense. To get submartingale convergence theorems,
we give sufficient conditions for the Kudo–Aumann integral and
Hiai–Umegaki conditional expectation to be closed both for compact
convex set valued random variables and for closed convex set valued random
variables. We also give an example of a bounded closed convex set valued random
variable whose Kudo–Aumann integral is not closed.
Publié le : 1998-07-14
Classification:
Set valued submartingale,
set valued supermartingale,
Kudo-Aumann integral,
Kuratowski-Mosco convergence,
60G42,
28B20,
60G48,
60D05
@article{1022855757,
author = {Li, Shoumei and Ogura, Yukio},
title = {Convergence of set valued sub- and supermartingales in the
Kuratowski-Mosco sense},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1384-1402},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855757}
}
Li, Shoumei; Ogura, Yukio. Convergence of set valued sub- and supermartingales in the
Kuratowski-Mosco sense. Ann. Probab., Tome 26 (1998) no. 1, pp. 1384-1402. http://gdmltest.u-ga.fr/item/1022855757/