For Markov chains, linear and nonlinear response to time-dependent forcings can be written as sums of exponentials governed by the chain's Koopman eigenvalues, enabling equation-free response prediction.
1982 Stochastic processes: Time evolution, symmetries and linear response.Physics Reports88, 207 – 319
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Interpretable and Equation-Free Response Theory for Complex Systems
For Markov chains, linear and nonlinear response to time-dependent forcings can be written as sums of exponentials governed by the chain's Koopman eigenvalues, enabling equation-free response prediction.