On Multivalued Amarts
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 93-99
MSC: 60G48, 60F15, 28B.
DOI: 10.4064/ba52-1-10
Abstract
In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space $B$ the fact that every $L^{1}$-bounded $B$-valued martingale converges a.s. in norm to an integrable $B$-valued random variable (r.v.) is equivalent to the Radon–Nikodym property [6]. In this paper we solve the problem of a.s. convergence of multivalued amarts by giving a topological characterization.
