Universität zu Köln

Faigle, Ulrich and Gierz, Gerhard (2018). Markovian statistics on evolving systems. Evol. Syst., 9 (3). S. 213 - 226. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1868-6486

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Abstract

A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes between the deterministic evolution of a system and the stochastic nature of observations on the evolving system. General Markov chains are defined in this context and it is shown how typical traditional models of classical or quantum random walks and Markov processes fit into the framework and how a theory of quantum statistics (sensu Barndorff-Nielsen, Gill and Jupp) may be developed from it. The framework permits a general theory of joint observability of two or more observation variables which may be viewed as an extension of the Heisenberg uncertainty principle and, in particular, offers a novel mathematical perspective on the violation of Bell's inequalities in quantum models. Main results include a general sampling theorem relative to Riesz evolution operators in the spirit of von Neumann's mean ergodic theorem for normal operators in Hilbert space.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Faigle, Ulrich UNSPECIFIED UNSPECIFIED UNSPECIFIED Gierz, Gerhard UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-175715
DOI:	10.1007/s12530-017-9186-8
Journal or Publication Title:	Evol. Syst.
Volume:	9
Number:	3
Page Range:	S. 213 - 226
Date:	2018
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1868-6486
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUANTUM RANDOM-WALKS; CHAINS; IDENTIFIABILITY Multiple languages Computer Science, Artificial Intelligence Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/17571