The Annals of Probability

Noise as a Boolean algebra of $\sigma$-fields

Boris Tsirelson

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A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of $\sigma$-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of $\sigma$-fields. The largest extension of such Boolean algebra of $\sigma$-fields, being well-defined always, is a complete Boolean algebra if and only if the noise is classical, which answers an old question of J. Feldman.

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Ann. Probab., Volume 42, Number 1 (2014), 311-353.

First available in Project Euclid: 9 January 2014

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Zentralblatt MATH identifier

Primary: 60G99: None of the above, but in this section
Secondary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx} 60G20: Generalized stochastic processes 60G60: Random fields

Black noise


Tsirelson, Boris. Noise as a Boolean algebra of $\sigma$-fields. Ann. Probab. 42 (2014), no. 1, 311--353. doi:10.1214/13-AOP861.

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