Ward, JA orcid.org/0000-0002-2469-7768 and López-García, M (2019) Exact analysis of summary statistics for continuous-time discrete-state Markov processes on networks using graph-automorphism lumping. Applied Network Science, 4. 108. ISSN 2364-8228
Abstract
We propose a unified framework to represent a wide range of continuous-time discrete-state Markov processes on networks, and show how many network dynamics models in the literature can be represented in this unified framework. We show how a particular sub-set of these models, referred to here as single-vertex-transition (SVT) processes, lead to the analysis of quasi-birth-and-death (QBD) processes in the theory of continuous-time Markov chains. We illustrate how to analyse a number of summary statistics for these processes, such as absorption probabilities and first-passage times. We extend the graph-automorphism lumping approach [Kiss, Miller, Simon, Mathematics of Epidemics on Networks, 2017; Simon, Taylor, Kiss, J. Math. Bio. 62(4), 2011], by providing a matrix-oriented representation of this technique, and show how it can be applied to a very wide range of dynamical processes on networks. This approach can be used not only to solve the master equation of the system, but also to analyse the summary statistics of interest. We also show the interplay between the graph-automorphism lumping approach and the QBD structures when dealing with SVT processes. Finally, we illustrate our theoretical results with examples from the areas of opinion dynamics and mathematical epidemiology.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | continuous-time Markov chain; stochastic process; network; graph-automorphism; lumping; summary statistics; absorption |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number MRC MR/N014855/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Sep 2019 14:06 |
Last Modified: | 18 Dec 2019 15:12 |
Status: | Published |
Publisher: | SpringerOpen |
Identification Number: | 10.1007/s41109-019-0206-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:150131 |
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