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A simple framework to justify linear response theory. (English) Zbl 1186.82006

Summary: 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.

MSC:

82B05 Classical equilibrium statistical mechanics (general)
37A60 Dynamical aspects of statistical mechanics
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
86A32 Geostatistics
86A10 Meteorology and atmospheric physics
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