Applications of Magnus expansions and pseudospectra to Markov processes

Iserles, A; MacNamara, S

Applications of Magnus expansions and pseudospectra to Markov processes

Iserles, A MacNamara, S

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Publication Type:: Journal Article
Citation:: European Journal of Applied Mathematics, 2019, 30 (2), pp. 400 - 425
Issue Date:: 2019-04-01

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Field	Value	Language
dc.contributor.author	Iserles, A	en_US
dc.contributor.author	MacNamara, S	en_US
dc.date.issued	2019-04-01	en_US
dc.identifier.citation	European Journal of Applied Mathematics, 2019, 30 (2), pp. 400 - 425	en_US
dc.identifier.issn	0956-7925	en_US
dc.identifier.uri	http://hdl.handle.net/10453/136233
dc.description.abstract	Copyright © 2018 Cambridge University Press. New directions in Markov processes and research on master equations are showcased by example. The utility of Magnus expansions for handling time-varying rates is demonstrated. The useful notion in applied mathematics often turns out to be the pseudospectra and not simply the eigenvalues. We highlight that general principle with our own examples of Markov processes where exact eigenvalues are found and contrasted with the large errors produced by standard numerical methods. As a motivating application, isomerisation provides a running example and an illustration of our approaches to chemical kinetics. We also present a brief example of a totally asymmetric exclusion process.	en_US
dc.relation.ispartof	European Journal of Applied Mathematics	en_US
dc.relation.isbasedon	10.1017/S0956792518000177	en_US
dc.subject.classification	Applied Mathematics	en_US
dc.title	Applications of Magnus expansions and pseudospectra to Markov processes	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	30	en_US
utslib.for	0102 Applied Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	30	en_US

Abstract:

Copyright © 2018 Cambridge University Press. New directions in Markov processes and research on master equations are showcased by example. The utility of Magnus expansions for handling time-varying rates is demonstrated. The useful notion in applied mathematics often turns out to be the pseudospectra and not simply the eigenvalues. We highlight that general principle with our own examples of Markov processes where exact eigenvalues are found and contrasted with the large errors produced by standard numerical methods. As a motivating application, isomerisation provides a running example and an illustration of our approaches to chemical kinetics. We also present a brief example of a totally asymmetric exclusion process.

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http://hdl.handle.net/10453/136233