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Gaussian processes and martingales for fuzzy valued random variables with continuous parameter. (English) Zbl 0988.60025
The purpose of this paper is to investigate fuzzy-valued Gaussian processes and martingales with continuous parameters. M. L. Puri and D. A. Ralescu [Ann. Probab. 13, 1373-1379 (1985; Zbl 0583.60011)] gave the first representation theorem for the fuzzy-valued random variables whose level sets are non-empty compact convex sets in \(\mathbb{R}^n\) by using the embedding method under the Lipschitz condition. The main result of the paper consists in rebuilding the embedding theorem, and proving the same representation theorem but for the fuzzy-valued random variables whose level sets are non-empty bounded closed convex sets in a separable Banach space, without the Lipschitz condition. Then this result is extended to the fuzzy-valued Gaussian processes and to the set-valued martingales.

MSC:
60G15 Gaussian processes
60G44 Martingales with continuous parameter
26E50 Fuzzy real analysis
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