Convergence Theorems for Generalized Random Variables and Martingales

We examine generalizations of random variables and martingales. We prove a new convergence theorem for setvalued martingales. We also generalize a well known characterization of set-valued random variables to the fuzzy setting. Keywords-- Banach space, fuzzy, martingale, random variable, set-valued. 1 Set-valued random variables and martingales The theory of conditional expectations and martingales has been established for Banach space-valued, Bochnerintegrable functions. Hiai and Umegaki have then generalized random variables, conditional expectations and martingales to the set-valued (multivalued) setting in [1]. We will assume that the reader is familiar with the basic ideas

• Type: Journal
• Year: 2009
• Where: EUSFLAT
• Authors: Andrew L. Pinchuck
• Keywords: Conditional Expectations, EUSFLAT 2009, Fuzzy Logic, Random Variables, Set-valued Random Variables