Response and sensitivity using markov chains

Santos Gutierrez, M. and Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471 (2020) Response and sensitivity using markov chains. Journal of Statistical Physics, 179 (5-6). pp. 1572-1593. ISSN 0022-4715 doi: 10.1007/s10955-020-02504-4

Abstract/Summary

Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the investigation of climate response to perturbations. In this respect, it is crucial to determine what the linear response of a system is as a quantification of sensitivity. Alongside previous work, here we use the transfer operator formalism to study the response and sensitivity of a dynamical system undergoing perturbations. By projecting the transfer operator onto a suitable finite dimensional vector space, one is able to obtain matrix representations which determine finite Markov processes. Further, using perturbation theory for Markov matrices, it is possible to determine the linear and nonlinear response of the system given a prescribed forcing. Here, we suggest a methodology which puts the scope on the evolution law of densities (the Liouville/Fokker–Planck equation), allowing to effectively calculate the sensitivity and response of two representative dynamical systems.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/88975
Identification Number/DOI	10.1007/s10955-020-02504-4
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE)
Publisher	Springer
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