Wasserstein Convergence Rates for Empirical Measures of Subordinated Processes on Noncompact Manifolds

平坦环面上从属分数布朗运动经验测度的Wasserstein收敛性

Wasserstein Convergence for Empirical Measures of Subordinated Fractional Brownian Motions on the Flat Torus

该研究估计平坦环面上从属分数布朗运动经验测度在所有p≥1的Wasserstein距离下的收敛速率，结果与现有相关研究一致，并拓展至时间离散化情形。

Wasserstein Convergence for Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds

We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\partial M$ to some reference measure, under the quadratic Wasserstein distance. For any initial distribution not concentrated on $\partial M$, we obtain the rate of convergence and even the precise limit for the conditional expectation of the quadratic Wasserstein distance conditioned on the process killed upon exiting $M\setminus\partial M$. In particular, the results coincide with the recent ones proved by F.-Y. Wang in \cite…

Wasserstein Convergence for Empirical Measures of Subordinated Diffusions on Riemannian Manifolds

Let $M$ be a connected compact Riemannian manifold possibly with a boundary, let $V\in C^2(M)$ such that $μ(\d x):=\e^{V(x)}\d x$ is a probability measure, where $\d x$ is the volume measure, and let $L=Δ+\nabla V$. The exact convergence rate in Wasserstein distance is derived for empirical measures of subordinations for the (reflecting) diffusion process generated by $L$.

从属过程经验测度在 $p$-Wasserstein 距离下的精确收敛速度

Exact rate of convergence for the empirical measure of a subordinated process in $p$-Wasserstein distance

本文研究紧 Riemann 流形上从属扩散的非对称跳过程经验测度，利用 Bernstein 型不等式与 PDE 方法得到 $p$-Wasserstein 距离精确收敛速度及二次情形重整化极限。

The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

We develop a new method for showing that a given sequence of random variables verifies an appropriate law of the iterated logarithm. Our tools involve the use of general estimates on multidimensional Wasserstein distances, that are in turn based on recently developed inequalities involving Stein matrices and transport distances. Our main application consists in the proof of the exact law of the iterated logarithm for the Hermite variations of a fractional Brownian motion in the critical case.

Wasserstein Convergence for Conditional Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds

The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the rate of convergence of conditional empirical measures associated to subordinated Dirichlet diffusion processes on a connected compact Riemannian manifold with absorbing boundary. We give the sharp rate of convergence for any initial distribution and prove the precise limit for a large class of initial distributions. We follow the basic idea of Wang, but all…