Quelques résultats de convergence des amarts multivoques dans les espaces de Banach (Some convergence results for multi-valued amarts in Banach spaces). (French) Zbl 0582.60008
Let E be a Banach space having a separable topological dual and \(P_{cfb}(E)\) the complete metric space of all closed convex bounded nonempty subsets of E. The concept of vector-valued amarts (martingales) is extended to the \(P_{cfb}(E)\)-valued case. The author proves some sufficient conditions for the weak (strong) almost sure convergence of \(P_{cfb}(E)\)-valued amarts (martingales).
MSC:
| 60B12 | Limit theorems for vector-valued random variables (infinite-dimensional case) |
| 60F15 | Strong limit theorems |
| 60G48 | Generalizations of martingales |
