4 papers · 1 filter
Dimension-free Convergence Rate in Sliced Wasserstein Distance for Empirical Measures of Markov Processes
Feng-Yu Wang
To derive dimension-free convergence rates of empirical measures for Markov processes on a Banach space, we adopt the sliced Wasserstein distance (SW distance) induced by a probabi…
Bi-Coupling Method and Applications
Panpan Ren, Feng-Yu Wang
By developing a new technique called the bi-coupling argument, we estimate the relative entropy between different diffusion processes in terms of the distances of initial distribut…
Exponential Convergence in Entropy and Wasserstein Distance for McKean-Vlasov SDEs
Panpan Ren, Feng-Yu Wang
The following type exponential convergence is proved for (non-degenerate or degenerate) McKean-Vlasov SDEs: $$W_2(μ_t,μ_\infty)^2 +{\rm Ent}(μ_t|μ_\infty)\le c {\rm e}^{-λt} \…
Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker-Planck Equations
Zhongmin Qian, Panpan Ren, Feng-Yu Wang
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficient…