Naslov
Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

Autori
Antown, Fadi ; Dragičević, Davor ; Froyland, Gary

Izvornik
Journal of statistical physics (0022-4715) 170 (2018), 6; 1051-1087

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Linear response ; Markov chain ; Transfer operator ; Invariant measure ; Observable ; Decay of correlations ; Ulam’s method ; Optimization

Sažetak
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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