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Almost sure convergence and decomposition of multivalued random processes. (English) Zbl 0943.60008

Let \(X\) be a separable Banach space and \(P_{f}(X)\) be the class of all nonempty closed subsets of \(X\). The authors extend some known convergence and (Riesz) decomposition results for random processes with values in Banach space to \(P_{f}(X)\)-valued processes (random sets). A variety of such multivalued processes is considered: submartingales, uniform amarts, weak sequential amarts and amarts of infinite order. The submartingale and uniform amarts cases of these results extend the well known convergence result of J. Neveu [Ann. Inst. Heinri Poincaré, n. Sér., Sect. B 8, 1-7 (1972; Zbl 0235.60010)].

MSC:

60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60G48 Generalizations of martingales
46G12 Measures and integration on abstract linear spaces
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections

Citations:

Zbl 0235.60010
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References:

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