With noise in the sense of i.i.d. random sequence, a noise is black if it is not isomorphic to standard Gaussian white noise.

Tsirelson showed the existence of black noise through the scaling limit of coalescing Brownian motion.

Watanabe gave a simpler example, also based on a coalescing stochastic flow, but using a singular diffusion.

Nelson, chap 18, showed how to construct a Brownian motion using non-standard analysis.

I'm wondering if someone tried to construct a black noise using non-standard method.

non-classicalif it is not isomorphic to standard Gaussian white noise, and black if it has no classical subnoise. – Tom Ellis Nov 18 '13 at 5:41