Applications of Magnus expansions and pseudospectra to Markov processes

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