B. Tsirelson

Noise as a Boolean algebra of sigma-fields

Recent works

Boris Tsirelson,
"Noise as a Boolean algebra of σ-fields"
The Annals of Probability 42:1, 311-353 (2014).
Available online via Project Euclid (not free, sorry):
or from my site: [download]
See also arXiv.org/abs/1111.7270/

A long (42 pages) research paper. Bibl. 22 refs.

A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of σ-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of σ-fields. The largest extension of such Boolean algebra of σ-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.

  1. Introduction.
  2. Main results.
  3. Preliminaries.
  4. Convergence of sigma-fields and independence.
  5. Noise-type completion.
  6. Classicality and blackness.
  7. The easy part of Theorem 1.5.
  8. The difficult part of Theorem 1.5.
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