Please use this identifier to cite or link to this item: http://hdl.handle.net/2381/20396
Title: Entropy: The Markov ordering approach
Authors: Gorban, Alexander N.
Gorban, P.A.
Judge, G.
First Published: 7-May-2010
Publisher: MDPI, Basel, Switzerland.
Citation: Entropy, 2010, 12 (5), pp. 1145-1193
Abstract: The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally “most random” distributions.
DOI Link: 10.3390/e12051145
eISSN: 1099-4300
Links: http://hdl.handle.net/2381/20396
http://www.mdpi.com/1099-4300/12/5/1145
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2010 by the authors; licensee MDPI, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license http://creativecommons.org/licenses/by/3.0/.
Appears in Collections:Published Articles, Dept. of Mathematics

Files in This Item:
File Description SizeFormat 
entropy-12-01145.pdfPublished (publisher PDF)538.67 kBAdobe PDFView/Open


Items in LRA are protected by copyright, with all rights reserved, unless otherwise indicated.