A simple framework to justify linear response theory

TL;DR

This paper provides a rigorous mathematical foundation for linear response theory in forced dissipative stochastic systems, enhancing its reliability for climate change modeling and other scientific applications.

Contribution

It develops a mathematically rigorous justification of linear response theory applicable to finite and infinite-dimensional systems in climate science and related fields.

Findings

Established a rigorous framework for linear response theory

Applicable to both finite and infinite-dimensional systems

Strengthens theoretical basis for climate change analysis

Abstract

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.