A dual eigenvector condition for strong lumpability of Markov chains

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Necessary and sufficient conditions for identifying strong lumpability in Markov chains are presented. We show that the states in a lump necessarily correspond to identical elements in eigenvectors of the dual transition matrix. If there exist as many dual eigenvectors that respect the necessary condition as there are lumps in the aggregation, then the condition is also sufficient. The result is demonstrated with two simple examples.
6 pages. Footnote 1 added

Keywords

Probability, 60J22 (Primary), 15A18, 60J99 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/158287

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.1986
 http://arxiv.org/abs/0710.1986

Collections

arXiv