Hypoelliptic entropy dissipation for stochastic differential equations
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866913689837240320 |
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| author | Feng, Qi Li, Wuchen |
| author_facet | Feng, Qi Li, Wuchen |
| contents | We study the convergence analysis for general degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to analyze the Fokker-Planck equation, in which the Lyapunov functional is chosen as a weighted relative Fisher information functional. We derive a structure condition and formulate the Lyapunov constant explicitly. We prove the exponential convergence result for the probability density function towards its invariant distribution in the $L_1$ distance. Two examples are presented: underdamped Langevin dynamics with variable diffusion matrices and three oscillator chain models with nearest-neighbor couplings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_00544 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hypoelliptic entropy dissipation for stochastic differential equations Feng, Qi Li, Wuchen Dynamical Systems Differential Geometry Probability We study the convergence analysis for general degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to analyze the Fokker-Planck equation, in which the Lyapunov functional is chosen as a weighted relative Fisher information functional. We derive a structure condition and formulate the Lyapunov constant explicitly. We prove the exponential convergence result for the probability density function towards its invariant distribution in the $L_1$ distance. Two examples are presented: underdamped Langevin dynamics with variable diffusion matrices and three oscillator chain models with nearest-neighbor couplings. |
| title | Hypoelliptic entropy dissipation for stochastic differential equations |
| topic | Dynamical Systems Differential Geometry Probability |
| url | https://arxiv.org/abs/2102.00544 |