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- W3161191763 abstract "The objects under inspection, on a given probability space, are noise(-type) Boolean algebras -- distributive non-empty sublattices of the lattice of all complete sub-$sigma$-fields, whose every element admits an independent complement. Special attention is given to the decompositions of the algebras of operators (acting on $mathrm{L}^2$) generated by the conditional expectations w.r.t. the members of said noise Boolean algebras. Atoms of the spectrum are identified in explicit terms. For a reverse filtration admitting an innovating sequence of equiprobable random signs, a discreteness property of the measure of the associated noise Boolean algebra is shown to imply product-typeness. Noise projections on the are introduced, which correspond to restricting a noise to a part of its domain space. They appear to play a natural (albeit technical) role in the general analysis. In particular, through them manifests itself the tensor structure of the decomposition. The spectrum is precisely delineated in the classical case (i.e. when the noise Boolean algebra is complete), a kind-of standard symmetric Fock space form thereof is procured. The latter result leads to a new characterization of classicality and blackness involving spectral independence." @default.
- W3161191763 created "2021-05-24" @default.
- W3161191763 creator A5026962152 @default.
- W3161191763 date "2021-05-12" @default.
- W3161191763 modified "2023-09-23" @default.
- W3161191763 title "A potpourri of results in the general theory of stochastic noises" @default.
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