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Noise as a Boolean algebra of \(\sigma\)-fields. (English) Zbl 1317.60066

Noises in the author’s sense may also be viewed in terms Boolean algebras of \(\sigma\)-subfields of a probability space (the decissive property is that the complement operation in this Boolean algebra sends a \(\sigma\)-subfields to another one that is independente of the first). Classicality of the noise means that the associated \(L^2\)-spaces have enough factorizing vectors. The author shows (among other useful insights) a conjecture by Feldman that the Boolean algebra is complete if and only of the noise is classical.

MSC:

60G99 Stochastic processes
60A10 Probabilistic measure theory
60G51 Processes with independent increments; Lévy processes
60G20 Generalized stochastic processes
60G60 Random fields
06E99 Boolean algebras (Boolean rings)
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References:

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