Characterisations of classes of multivalued processes using Riesz approximations

Sitadri N. Bagchi

Journal of Multivariate Analysis, 1992, vol. 42, issue 1, 23-34

Abstract: Let E' be the separable dual of a Banach space E, and the class of all nonempty, convex, weak*-compact subsets od E'. J. Neveu proved the convergence of -valued martingales called multivalued martingales. We prove Riesz approximations for some multivalued processes; i.e., for these processes, we show that they are close to some multivalued martingales. We also obtain Riesz decomposotions of some single-valued processes; i.e., we show that they are the sums of a martingale and another process which goes to zero. The class of processesses considered for Riesz approximation includes multivalued amarts. The Riesz decomposition of single-valued amarts was obtained by Edgar and Sucheston. Our proofs require some of their results in the multivalued form. Riesz decomposition for multivalued processes is not possible even in simple cases.

Keywords: Hausdorff's; metric; multivalued; random; variable; (mrv); multivalued; process; multivalued; martingale; multivalued; amart; multivalued; amart; of; order; d; multivalued; i-amart; Pettis; distance; Riesz; decomposition; Riesz; approximation; Radon-Nikodym; property (search for similar items in EconPapers)
Date: 1992
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