Within and beyond the reach of Brownian innovation (Q1126823)

A system whose time evolution is random is often described by a deterministic system under independent random influences. In this way, complicated statistical correlations are reduced to a deterministic mechanism (perhaps still complicated) together with a stochastic but uncorrelated noise. ``That'', says the author, ``is the idea of innovation''. More precisely, an innovation is defined as a real-time transformation of a noise into a given random process. Some surprising results (such as the appearance of information from thin air) are presented, and processes having no innovations are discussed. Some open questions are stated, and a long list of references is provided.