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Information Gamma calculus: Convexity analysis for stochastic differential equations

Event Category:
Reading Seminar on Mathematics of Machine Learning
Wuchen Li
University of South Carolina

We study the Lyapunov convergence analysis for degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to 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 Lypapunov constant explicitly. Given the positive Lypapunov constant, we prove the exponential convergence result for the probability density function towards its invariant distribution in the L1 norm. Several examples are presented: underdamped Langevin dynamics with variable diffusion matrices and three oscillator chain models with nearest-neighbor couplings, and underdamped mean field Langevin dynamics (weakly self-consistent Vlasov-Fokker-Planck equations).

Friday, September 15, 2023 - 10:00am
LGRT 1685 and Zoom: