Journal of the
Korean Mathematical Society JKMS

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and sub- and super- martingales. These kinds of martingales, sub- and super-martingales are the extension of classical real valued martingales, sub- and super-martingales. Here we compare two kinds of convergences, in the Hausdorff metric and in the Kuratowski-Mosco sense. We also introduce a new convergence for the fuzzy valued case in the graph sense and obtain convergence theorems.

Keywords: set valued martingale, fuzzy valued martingale, sub-, super-martingale, the Kuratowski-Mosco convergence

MSC numbers: 60G42, 28B20, 60G48, 60D05