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Within and beyond the reach of Brownian innovation. (English) Zbl 0907.60053

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.
Reviewer: A.Dale (Durban)

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G07 General theory of stochastic processes
60J65 Brownian motion
60G35 Signal detection and filtering (aspects of stochastic processes)
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