Linear Response Theory for Nonlinear Stochastic Differential Equations with $\alpha$-stable L\'{e}vy Noises

Qi Zhang; Jinqiao Duan

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arXiv · 2008.06394

Linear Response Theory for Nonlinear Stochastic Differential Equations with $\alpha$-stable L\'{e}vy Noises

Qi Zhang·Jinqiao Duan

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Abstract

We consider a nonlinear stochastic differential equation driven by an $\alpha$-stable L\'{e}vy process ($1<\alpha<2$). We first obtain some regularity results for the probability density of its invariant measure via establishing the a priori estimate of the corresponding stationary Fokker-Planck equation. Then by the a priori estimate of Kolmogorov backward equations and the perturbation property of Markov semigroup, we derive the response function and generalize the famous linear response theory in nonequilibrium statistical mechanics to non-Gaussian stochastic dynamic systems.

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BibTeX RIS

Qi Zhang, Jinqiao Duan. 2020-08-14. Linear Response Theory for Nonlinear Stochastic Differential Equations with $\alpha$-stable L\'{e}vy Noises. https://arxiv.org/abs/2008.06394

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