Within and beyond the reach of Brownian innovation
type: Item
instance of: scholarly article
title: Within and beyond the reach of Brownian innovation
zbMATH Open document ID: 0907.60053
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/227669
full work available at URL: Tsirelson.MAN.html
review text: 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.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 1184370
zbMATH Keywords: innovation
zbMATH Keywords: filtration
author: B. S. Tsirel'son
reviewed by: Andrew Dale
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184370