Convergence theorems for set-valued martingales and semimartingales
We continue our study of set-valued random processes, initiated in our previous works. In particular, we prove new stronger convergence and representation theorems for set-valued martingales and semimartingales, extending this way results existing in the literature. In the last two decades the subject of set-valued random processes has attracted the interest of several mathematicians. Also it was illustrated that set- valued random processes arise naturally in problems of optimization, of uncertain information systems, and of mathematical economics. We present two new convergence theorems. The first is for set-valued semimartingales, while the second is for set-valued martingales. In addition, both theorems also include regularity results.
scientific article; zbMATH DE number 404548
scientific article