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Applications of Magnus expansions and pseudospectra to Markov processes

Published online by Cambridge University Press:  17 April 2018

A. ISERLES  and
S. MACNAMARA
A. ISERLES
Affiliation:
Department of Applied Mathematics and Mathematical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK email: a.iserles@damtp.cam.ac.uk
S. MACNAMARA
Affiliation:
Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, Australia email: shev.macnamara@uts.edu.au
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Abstract

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.

Keywords

60J2860H3565F40
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 2 , April 2019 , pp. 400 - 425
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

†This research and Shev MacNamara have been partially supported by a David G. Crighton Fellowship to DAMTP, Cambridge.

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