Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker-Planck Equations

Zhongmin Qian; Panpan Ren; Feng-Yu Wang

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arXiv · 2308.16373

Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker-Planck Equations

Zhongmin Qian·Panpan Ren·Feng-Yu Wang

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Abstract

The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and exponential ergodicity in entropy are derived for distribution dependent stochastic Hamiltonian systems associated with nonlinear kinetic Fokker Planck equations.

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Zhongmin Qian, Panpan Ren, Feng-Yu Wang. 2023-08-31. Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker-Planck Equations. https://arxiv.org/abs/2308.16373

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