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

Abstract

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.

Published in at http://dx.doi.org/10.1214/13-AOP861 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• On the scaling limits of planar percolation
• Nonclassical stochastic flows and continuous products
• Scaling Limit, Noise, Stability
• The Brownian web is a two-dimensional black noise

Cited by in corpus (4)

• The Brownian web is a two-dimensional black noise
• Arithmetic of (independent) sigma-fields on probability spaces
• Random compact set meets the graph of nonrandom continuous function
• A potpourri of results in the general theory of stochastic noises