Hypoelliptic entropy dissipation for stochastic differential equations

Abstract

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.

Typos corrected. 50 pages, 4 figures

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Cited by in corpus (1)

• The log-Sobolev inequality for spin systems of higher order interactions