Kantorovich-Rubinstein Distance and Approximation for Non-local Fokker-Planck Equations

Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry

A Poisson or a binomial process on an abstract state space and a symmetric function $f$ acting on $k$-tuples of its points are considered. They induce a point process on the target space of $f$. The main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a Poisson process on the target space. The technical background are a version of Stein's method for Poisson process approximation, a Glauber dynamics representation for the Poisson process and the Malliavin formalism. As applications of the main result, error …

相对最优传输

Relative Optimal Transport

本文提出相对最优传输理论，基于特定子集作为质量库，比较不同总变分的测度。研究了相对Kantorovich-Rubinstein范数、Wasserstein距离及对偶性，并证明了Riesz-Markov-Kakutani定理的相对版本。

Stein's method and Papangelou intensity for Poisson or Cox process approximation

In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a measure and another finite point process is bounded by the $L^1$-distance between their respective Papangelou intensities. Then, we deduce some convergence rates for sequences of point processes approaching a Poisson or a Cox point process.

用于偏微分方程的蒙日-康托罗维奇距离：耦合方法

Monge-Kantorovich distance for PDEs: the coupling method

该研究非正式回顾了多类偏微分方程（如热方程、福克-普朗克方程等），通过构建解的耦合（变量加倍）证明其解对的蒙日-康托罗维奇距离衰减，还补充了多孔介质方程的处理思路及对偶问题方法。

环面上动理学Fokker-Planck方程的平衡态收敛性

Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus

该研究针对环面上的动理学Fokker-Planck方程，通过求解随机微分方程证明其在$\u202fW_2$距离下指数收敛至平衡态，还发现共适应耦合下的收敛界需依赖初始距离的平方根。

带有Lévy噪声的粘性能量壳模型在Wasserstein距离下的截断遍历界

Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise

本文为带有随机能量注入的粘性能量壳格点湍流模型，在重整化WKR距离下建立了显式非渐近遍历界，系统可由多种Lévy过程驱动，基于Bessel函数卷积的解表示证明了渐近急剧热化。

$\mathrm{P}_2(\mathbb{R}^d)$ 中 Zolotarev 距离与 Wasserstein 距离之间的尖锐不等式

Sharp inequalities between Zolotarev and Wasserstein distances in $\mathrm{P}_2(\mathbb{R}^d)$

基于新的Kantorovich-Rubinstein对偶原理，本文将将将Rio不等式最优扩展至任意维度，并为具有指定方差的中心化概率下Zolotarev距离与Wasserstein距离的比值提出最优上界。

Poisson process approximation under stabilization and Palm coupling

We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic geometry. Our bounds are derived for the Kantorovich-Rubinstein distance using the generator approach to Stein's method. We give different types of bounds for different point processes. While some of our bounds are given in terms of coupling of the point process with its Palm version, the others are in terms of the local dependence structure formalized via the n…

Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems

In this paper, we develop a natural operator-splitting variational scheme for a general class of non-local, degenerate conservative-dissipative evolutionary equations. The splitting-scheme consists of two phases: a conservative (transport) phase and a dissipative (diffusion) phase. The first phase is solved exactly using the method of characteristic and DiPerna-Lions theory while the second phase is solved approximately using a JKO-type variational scheme that minimizes an energy functional with respect to a certain Kantorovich optimal transport cost functional. In addition, we also introduce …

高斯空间上Sobolev映射律之间总变差距离的估计

Estimates of the total variation distance between laws of Sobolev mappings on Gaussian spaces

研究高斯空间上\(\mathbb{R}^k\)值Sobolev映射律间总变差距离，利用Malliavin行列式小球界，通过Kantorovich - Rubinstein距离等估计，基于分数正则性估计证明，为特定随机向量分布提供新估计及更高指数。

中心极限定理中运输距离的估计

Estimates of transport distance in the central limit theorem

本文研究了中心极限定理中运输距离的估计，提出了更精确的边界值结果，并扩展到多变量情况。

全超线性增长 McKean-Vlasov SDE 及其粒子系统的驯服 Euler 逼近：强混沌传播、收敛性与遍历性的尖锐速率

Tamed Euler approximation for fully superlinear growth McKean-Vlasov SDE and their particle systems: sharp rates for strong propagation of chaos, convergence and ergodicity

针对全变量超线性增长的 McKean–Vlasov SDE 及粒子系统，论文提出全显式驯服 Euler 格式，证明适定性、维数一致的 N^{-1/2} 混沌传播速率、1/2 强收敛速率及指数遍历性。