A simple framework to justify linear response theory

By Martin Hairer, Andrew J. Majda. Nonlinearity, 2009

164 citations recorded by the source corpus.

The use of linear response theory for forced dissipative stochastic dynamical systems through the fluctuation dissipation theorem is an attractive way to study climate change systematically among other applications. Here, a mathematically rigorous justification of linear response theory for forced dissipative stochastic dynamical systems is developed. The main results are formulated in an abstract setting and apply to suitable systems, in finite and infinite dimensions, that are of interest in climate change science and other applications.

Subfields: Economics and Econometrics, Global and Planetary Change, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/159f47bffcc0e96876456688abe1040a1c81e049

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In Economics and Econometrics

In Global and Planetary Change

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Citations in the corpus

Challenges in Climate Science and Contemporary Applied Mathematics (2012, background): “The recent paper [45] only begins the mathematically rigorous analysis of fluctuation-dissipation theorems for turbulent dynamical systems.”
Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions (2011, methodology): “This is inspired by constructions in [21, 22].”
Stochastic climate dynamics: Random attractors and time-dependent invariant measures (2011, background): “A mathematically rigorous justification of linear response theory for forced dissipative stochastic dynamical systems has been developed recently in [89].”
Linear response, or else (2014, methodology): “9See the work of Hairer and Majda [25].”