Weak Convergence of Probability Measures

概率空间的齐雷尔森卷积系统的收敛性

Convergence of Tsirelson convolution systems of probability spaces

研究概率空间的齐雷尔森卷积系统，通过关联特定射影系统，探讨其收敛性与K收敛性，分析它们之间关系及与希尔伯特空间双参数积系统联系，揭示收敛卷积系统产生概率空间连续积，K收敛的产生流系统。

Uniform decomposition of probability measures: quantization, classification, rate of convergence

The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an elementary construction of a uniform decomposition of probability measures in dimension $d\geq 1$. This decomposition is then used to give upper-bounds on the rate of convergence of the optimal uniform approximation error. These bounds appear to be the generalization of the ones obtained in (Xu and Berger, 2017) and to be sharp for generic probability measur…

关于随机逼近的收敛性、锁定概率和样本复杂性

On the convergence, lock-in probability and sample complexity of stochastic approximation

证明了在标准假设下，如果随机逼近迭代保持紧，则它们以概率1收敛到它们的o. d. e。极限提示一个简单的密封性测试（因此，收敛）。此外，对锁定概率的估计，即，收敛到O.D.E.的特定吸引子的概率限制给定的迭代访问其吸引区域和样本复杂性，即，还提供了在具有规定概率的期望极限集的规定邻域内所需的步数。后者改进显着现有的结果，因为他们需要一个更弱的条件，鞅差噪声。

非交换概率中随机和的收敛性

Convergence of random sums in non-commutative probability

研究非交换概率空间中自伴变量随机和的收敛性，通过建立*收敛结果，证明联合*收敛与停止随机变量矩及均值方差比收敛的等价性，得到多种变量随机和的中心极限定理及缩放*收敛极限。

具有上Fell拓扑的超空间上概率测度的弱收敛

Weak convergence of probability measures on hyperspaces with the upper Fell-topology

本文研究局部紧第二可数Hausdorff空间中赋予Fell、上Fell及上Vietoris拓扑的超空间上概率测度的弱收敛，重点探讨上Fell拓扑，并将其结果应用于随机闭集分布收敛及可测选择的渐近行为。

随机级数的收敛性与博弈概率中强大数律的收敛速率

Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability

在Shafer和Vovk（2001）的博弈论概率框架下，给出了随机级数收敛性和强大数律收敛速度的统一处理.我们认为游戏的二次对冲以及更一般的弱对冲。后者对应于存在一个绝对矩的顺序小于二的测量理论框架。证明了中心随机序列的收敛性与套期保值价格序列的收敛性之间的精确关系。当解释在测度理论框架下，这些结果的收敛性的一个鞅的条件绝对矩序列的收敛性。为了证明这些结果，我们得出一些基本结果的现实，谁是一个球员在协议的博弈论概率的确定性策略。这是特别感兴趣的，因为现实的策略没有任何对应的测量理论框架，但他们可以用来证明结果，这可以解释在测量理论框架。

斜反射漫射的Weak Convergence

Weak Convergence of Obliquely Reflected Diffusions

Burdzy和Chen（1998）证明了多维正反射布朗运动的弱收敛性.我们推广他们的工作，考虑斜反射扩散过程。我们要求域的弱收敛，这比Wijsman拓扑中的收敛强，但比Hausdorff拓扑中的收敛弱。

$n$ -粒子系统双线性型的Mosco型收敛性和Weak Convergence

Mosco Type Convergence of Bilinear Forms and Weak Convergence of $n$-Particle Systems

众所周知，Mosco（型）收敛是检验随机过程序列有限维分布弱收敛的一个工具。在本文中，我们关注的概念，Mosco型收敛的非对称随机过程，特别是$n$ -粒子系统，以建立相对紧性。

Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification: Extensions to $L^p$

A previous study analyzed the convergence of probability densities for forward and inverse problems when a sequence of approximate maps between model inputs and outputs converges in $L^\infty$. This work generalizes the analysis to cases where the approximate maps converge in $L^p$ for any $1\leq p < \infty$. Specifically, under the assumption that the approximate maps converge in $L^p$, the convergence of probability density functions solving either forward or inverse problems is proven in $L^q$ where the value of $1\leq q<\infty$ may even be greater than $p$ in certain cases. This greatly ex…

博弈论概率中强大数律收敛速率与贝叶斯先验集中速度的关系

Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability

本文研究了在博弈论概率下的单边无界预测博弈中，固定比例连续贝叶斯混合策略的资本过程的行为。建立了自正规化形式的强大数律的收敛速率与先验密度在原点附近发散到无穷远的速度之间的关系。特别是，我们目前的先验密度，确保有效性的Erdos-Feller-Kolmogorov-Petrowsky法律的重对数。

希尔伯特空间中Levy驱动卷积积分的非标准Skorokhod收敛性

Non-standard Skorokhod convergence of Levy-driven convolution integrals in Hilbert spaces

研究了Hilbert值$\int_0^t F_γ(t-s)\,d L(s)$型随机卷积积分在非标准$M_1$ Skorokhod拓扑中依概率收敛于由Lévy过程$L$驱动的过程$\int_0^t F(t-s)\, d L(s)$.在Banach空间中，我们引入了$M_1$ -收敛的强、弱和乘积模式，利用有限维边缘函数的依概率收敛和相应的振荡函数的良好性态，证明了随机连续卷积过程的$M_1$ -依概率收敛的一个判别准则，并建立了Lévy驱动随机卷积的依概率收敛的判别准则.该理论被应用到无穷维积分Ornstein-Uhlenbeck过程与对角化的生成元。

Weak convergence of Euler scheme for SDEs with singular drift

In this paper, we investigate the weak convergence rate of Euler-Maruyama's approximation for stochastic differential equations with irregular drifts. Explicit weak convergence rates are presented if drifts satisfy an integrability condition including discontinuous functions which can be non-piecewise continuous or in fractional Sobolev space.

广义Wasserstein距离与次线性期望的weak convergence

Generalized Wasserstein distance and weak convergence of sublinear expectations

本文定义了Borel概率测度集的广义Wasserstein距离，并证明了次线性期望的弱收敛可以用这个距离来刻画.

R^{K}上具有公共边缘的规律的Weak Convergence

Weak Convergence of Laws on R^{K} with Common Marginals

我们提出了一个拓扑等价的积分度量（Rachev，1991，Muller，1997），度量弱收敛的法律与共同的边缘。这个结果与应用有关，如几个简单的例子所示。

A weak convergence result for sequential empirical processes under weak dependence

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $α$-mixing sequence of random variables. In particular the uniformly boundedness assumption on the function class, which is required in most of the existing literature, is spared. Furthermore under strict stationarity a weak convergence result for the sequential empirical process indexed in function classes is obtained, as a direct consequence. Two examples in mathematical statistics, that cannot be treated with existing results, are given as po…

概率中$γ$阶的统计收敛性的一个概念--$αβ$

A notion of $αβ$-statistical convergence of order $γ$ in probability

一个实数序列$\{x_{n}\}_{n\in \mathbb{N}}$被称为$αβ$ -$γ$阶的统计收敛如果对于每个$δ>0,$ $$\underset{n\rightarrow \infty} {\lim} \frac{1}{(β_{n} - α_{n} + 1)^γ}~ |\{k \in [α_n,β_n] : |x_{k}-x|\geq δ\}|=0.$$，其中$\{α_{n}\}_{n\in \mathbb{N}}$和$\{β_{n}\}_{n\in \mathbb{N}}$是两个正实数序列，使得$\{α_{n}\}_{n\in \mathbb{N}}$和$\{β_{n}\}_{n\in \mathbb{N}}$都是非减的，$β_{n}\geq α_{n}$ $\forall ~n\in \mathbb{N},$（$β_{n}-α_{n})\rightarrow \infty$ as $n\rightarrow \infty.$本文研究了一个相关的收敛概念，其中$|x_{k}-x|$值分别用$P(|X_{k}-X|\geq \varepsilon)$和$E(|X_{k}-X|^{r})$代替（其中$X, X_k$是每个$k\in \mathbb{N}$的随机变量，$\varepsilon>0$，$P$表示概率，$E$表示期望），我们分别称它们为$αβ$ -概率中$γ$阶的…

基于双线性型的$n$ -粒子系统的Weak Convergence

Weak Convergence of $n$-Particle Systems Using Bilinear Forms

本文讨论了$n$ -粒子过程到确定平稳轨道的弱收敛性，即$n\to\infty$ .引入了一类双线性型的Mosco型收敛性.双线性型的Mosco型收敛性导致了$n$ -粒子系统的预解式的某种收敛性.在此基础上，建立了不变测度弱收敛的判别准则。在附加条件下，证明了平稳$n$ -粒子过程弱收敛于平稳确定性路径.该方法适用于粒子近似的Ginzburg-Landau型扩散。本文件与Löbus文件（2011/2012）密切相关。介绍了双线性型的不同定义和Mosco型收敛的不同形式。这两篇论文都证明了收敛形式和收敛类型的选择与特定的粒子系统有关。

随机演化系统的平均原理下的weak convergence

On weak convergence for stochastic evolutionary systems in average principle

证明了随机演化系统弱收敛于平均演化系统。使用R.Liptser在半鞅中提出的方法。但我们应用了一个奇异扰动问题的解来代替遍历定理。

加性Lévy噪声驱动下随机偏微分方程Galerkin逼近的Weak convergence

Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise

本文研究了Lévy噪声驱动的随机偏微分方程的弱逼近问题。手头的SPDE是抛物线与加性噪声过程。给出了相应的Galerkin逼近的弱收敛速度。收敛结果是通过使用Malliavin导数而不是通过Kolmogorov向后方程的普通方法导出的。

一般一维动力学方程概率值解的weak convergence特征

Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations

对于最近提出的一类一般非弹性Kac型方程，本文研究了其概率值解的长时间行为。特别地，本文给出了使相应的解收敛于平衡点的初始数据的充要条件。的证明依赖于一般的CLT的独立被加数适用于一个合适的Skorokhod表示的原始解决方案，评估在一个不断增加和发散序列的时间。结果表明，粗略地说，初始数据必须属于一个稳定定律的标准吸引区域，而平衡则可以表示为稳定定律的混合。

Fleming-Viot过程有限选举模型的弱原子收敛性

Weak atomic convergence of finite voter models toward Fleming-Viot processes

考虑了大有限集上带突变的多类型选举模型的经验测度，证明了它们在Fleming-Viot过程上的弱原子收敛性.弱原子拓扑中的收敛性强到足以回答Aldous（2013）提出的关于类型的相应熵过程和多样性过程的分布的一系列问题。

序列马尔可夫链蒙特卡罗方法的收敛性：I.概率测度的非线性流

Convergence of sequential Markov Chain Monte Carlo methods: I. Nonlinear flow of probability measures

序贯蒙特卡罗抽样算法是一类用于蒙特卡罗积分估计的随机算法。概率分布，它结合了马尔可夫链蒙特卡罗方法和重要性抽样/重新抽样方案的元素。我们开发了一个稳定性分析的非线性流的概率测度描述的粒子数趋于无穷大的算法的极限行为的功能不等式。稳定性结果来自全球和当地的假设下的发电机的基本大都市动态。这使我们能够证明，组合方法有时具有良好的渐近稳定性属性，在多模态设置，传统的MCMC方法混合非常缓慢。例如，这适用于所有温度下的平均场伊辛模型。

弱对数Sobolev不等式与熵收敛

Weak logarithmic Sobolev inequalities and entropic convergence

本文引入并研究了对数Sobolev不等式的一种弱化形式，并结合其它各种函数不等式（弱Poincaré不等式，一般Beckner不等式.）我们还讨论了对称扩散半群上相对熵的定量行为。特别地，我们给出了一个例子，其中Poincaré不等式不能用于导出熵收敛，而弱对数Sobolev不等式确保了结果。

Vervaat的Weak convergence和Vervaat长相关序列的误差过程

Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

继CsörgIgn，Szyszkowicz和王（安。{ \bf 34}，（2006），1013- 1044），我们考虑一个长范围相关的线性序列。证明了一致Vervaat误差过程和一致Vervaat误差过程的弱收敛性，并将其结果推广到具有无界支撑的分布，去掉了正态性假设。

Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

Our aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale related to the state indicator function, we provide sufficient conditions for weak convergence of stochastic integrals with re…

概率意义下紧集上一致收敛性及其在核空间对偶空间中随机分析的应用

Convergence Uniform on Compacts in Probability with Applications to Stochastic Analysis in Duals of Nuclear Spaces

该研究针对核空间强对偶空间上的连续/右连左极值过程序列，提出概率紧集一致收敛的充分条件，并通过半鞅空间拓扑性质、半鞅驱动线性随机演化方程解的收敛性两类应用验证了结果有效性。

Uniform approximation in classical weak convergence theory

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some scenarios where stronger results are needed in order to establish an asymptotic normal approximation uniformly over a family of probability measures. In this note we collect some results in this direction. We restrict ourselves to weak convergence in $\mathbb R^d$ with continuous limit measures.

关于Ky Fan度量在概率中粗理想收敛作用的研究

On the role of the Ky Fan metric in rough ideal convergence in probability

本文研究了Ky Fan度量在概率中粗理想收敛的作用，提出强弱粗理想聚点概念，并表征了最大可接受理想。

Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients

In this paper, by using Girsanov's transformation and the property of the corresponding reference stochastic differential equations, we investigate weak existence and uniqueness of solutions and weak convergence of Euler-Maruyama scheme to stochastic functional differential equations with Hölder continuous drift driven by fractional Brownian motion with Hurst index $H\in (1/2,1)$.

关于拟无穷可分律的弱收敛性

On weak convergence of quasi-infinitely divisible laws

本文研究了拟无穷可分律的弱收敛准则，在自然假设下将其弱收敛与 Lévy--Khinchine 谱函数的一种特殊收敛联系起来，补充了 Lindner、Pan 和 Sato（2018）的已知结果。

Characterization of probability distribution convergence in Wasserstein distance by $L^{p}$-quantization error function

We establish conditions to characterize probability measures by their $L^{p}$-quantization error functions in both $\mathbb{R}^{d}$ and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic (convergence for the $L^p$-Wasserstein distance). We first propose a criterion on the quantization level $N$, valid for any norm on $\mathbb{R}^{d}$ and any order $p$ based on a geometrical approach involving the Voronoï diagram. Then, we prove that in the $L^2$-case on a (separable) Hilbert space, the condition on the level $N$ can be reduced to $N=2$, whic…

退化扩散过程收敛速度的弱Poincaré不等式

Weak Poincaré Inequalities for Convergence Rate of Degenerate Diffusion Processes

对于可分希尔伯特空间上的压缩$C_0$ -半群，利用生成元的对称和反对称部分的弱Poincaré不等式估计了其衰减率.作为应用，对一类退化扩散过程的非指数收敛速度进行了刻划，从而推广了亚纯性的研究。提出了具体的例子。

全耦合多尺度随机微分方程在α-稳定过程中强收敛性和弱收敛性的收敛率

Strong and weak convergence rates for fully coupled multiscale stochastic differential equations driven by $α$-stable processes

本文研究了由α-稳定过程驱动的全耦合多尺度随机微分方程的强弱收敛率，通过非局部泊松方程构造校正方程以消除非齐次项，揭示了强弱收敛阶与Holder正则性条件的关系。

Levy过程驱动的非退化偏微分方程弱Euler逼近的收敛速率

On the Rate of Convergence of Weak Euler Approximation for Nondegenerate SDEs Driven by Levy Processes

研究了具有Hoelder连续系数的Levy过程驱动的偏微分方程解的弱Euler逼近的收敛速率。它调查的依赖率的规律性系数和驱动过程。所考虑的方程具有由球对称稳定过程驱动的非退化主部。

Strong and weak convergence rates for slow-fast stochastic differential equations driven by $α$-stable process

In this paper, we study the averaging principle for a class of stochastic differential equations driven by $α$-stable processes with slow and fast time-scales, where $α\in(1,2)$. We prove that the strong and weak convergence order are $1-1/α$ and $1$ respectively. We show, by a simple example, that $1-1/α$ is the optimal strong convergence rate.

Deferred Norlund statistical convergence in probability, mean and distribution for sequences of random variables

We introduce and study deferred Nörlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin type theorems for the sequence of random variables via deferred Nörlund statistically convergence and present compelling examples to demonstrate the effectiveness of the results.

Weak convergence of path-dependent SDEs with irregular coefficients

In this paper we develop via Girsanov's transformation a perturbation argument to investigate weak convergence of Euler-Maruyama (EM) scheme for path-dependent SDEs with Hölder continuous drifts. This approach is available to other scenarios, e.g., truncated EM schemes for non-degenerate SDEs with finite memory or infinite memory. Also, such trick can be applied to study weak convergence of truncated EM scheme for a range of stochastic Hamiltonian systems with irregular coefficients and with memory, which are typical degenerate dynamical systems. Moreover, the weak convergence of path-dependen…

Weak convergence of the extremes of branching Lévy processes with regularly varying tails

In this paper, we study the weak convergence of the extremes of supercritical branching Lévy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, $\mathbb{X}_t$ converges weakly. As a consequence, we obtain a limit theorem for the order statistics of $\mathbb{X}_t$.

一类季节性随机传染病模型的Weak Convergence

Weak Convergence of a Seasonally Forced Stochastic Epidemic Model

本文推广了Kurtz（1970，1971）的结果，证明了具有显式时间依赖性的传染病过程的弱收敛性，特别是当传播参数$β(t)$具有时间依赖性时.我们首先证明了当总体规模趋于无穷大时，时间非齐次过程弱收敛到平均场常微分方程的解。我们的第二个结果是，在适当的标度下，中心极限型波动收敛到一个扩散过程。

在概率局部收敛下度-度度量的极限行为

Limiting Behavior of Degree-Degree Metrics under Local Convergence in Probability

本文研究了随机图中度-度相关度量在概率局部收敛下的极限行为，并推导了非均质随机图和随机几何图中的相关度量显式表达式。

Weak convergence and tightness of probability measures in an abstract Skorohod space

In this article, we introduce the space $D([0,1];D)$ of functions defined on $[0,1]$ with values in the Skorohod space $D$, which are right-continuous and have left limits with respect to the $J_1$ topology. This space is equipped with the Skorohod-type distance introduced in Whitt (1980). Following the classical approach of Billingsley (1968, 1999), we give several criteria for tightness of probability measures on this space, by characterizing the relatively compact subsets of this space. In particular, one of these criteria has been used in the recent article Balan and Saidani (2018) for pro…

正则Dirichlet子空间的Weak convergence

Weak convergence of regular Dirichlet subspaces

本文证明了具有单调特征集的正则子空间的伴随扩散过程对于固定Dirichlet型的弱收敛性。更精确地说，给定一个固定的一维扩散过程及其正则子空间序列，如果正则子空间的特征集是减的或增的，则它们的相关扩散过程弱收敛于另一个扩散过程。这是[13]的一个推广结果。

$μ$-可积函数与有限测度的弱收敛

$μ$- Integrable Functions and Weak Convergence of Finite Measures

本文研究度量空间上取值于完备仿范向量空间或巴拿赫空间的$μ$-可积函数，给出有限测度弱收敛的若干充要条件。

几何概率中随机测度的收敛性

Convergence of random measures in geometric probability

给定$n$独立随机标记的$d$-向量$X_i$具有共同密度，定义测度$ν_n = \sum_i ξ_i $，其中$ξ_i$是由$X_i$附近的点的（适当重新缩放的）集合确定的测度（不一定是点测度）。从技术上讲，这意味着$ξ_i$以稳定半径尾部的适当幂律衰减稳定。对于$R^d$上的有界测试函数$f$，给出了$ν_n(f)$的一个大数定律和中心极限定理.后者意味着弱收敛的$ν_n(\cdot)$，适当的缩放和集中，高斯场作用于有界的测试功能。最后给出了一般性结果，并应用于无限晶粒尺寸的胚粒模型的体积和表面度量。

Weak convergence of Euler-Maruyama's approximation for SDEs under integrability condition

This work establishes the weak convergence of Euler-Maruyama's approximation for stochastic differential equations (SDEs) with singular drifts under the integrability condition in lieu of the widely used growth condition. This method is based on a skillful application of the dimension-free Harnack inequality. Moreover, when the drifts satisfy certain regularity conditions, the convergence rate is estimated. This method is also applicable when the diffusion coefficients are degenerate. A stochastic damping Hamiltonian system is studied as an illustrative example.

多维空间中马氏随机演化的Weak convergence

Weak convergence of Markovian random evolution in a multidimensional space

研究了$\mathbf{R}^n$中的马尔可夫对称性和非对称性随机演化。利用演化生成元的奇异扰动问题证明了马氏对称随机演化到Wiener过程和马氏非对称随机演化到漂移扩散过程的弱收敛性.在$\mathbf{D}_{\mathbf{R}^n\timesΘ}[0,\infty)$的马尔可夫随机演化的家庭的相对紧性也显示。

用weak convergence方法研究弱相互作用过程的大偏差性质

Large deviation properties of weakly interacting processes via weak convergence methods

本文研究了由伊藤随机微分方程（SDEs）模型描述的弱相互作用粒子系统的大偏差性质。已知在一定条件下，当粒子数趋于无穷大时，相应的经验测度序列收敛于相关的McKean-Vlasov方程的弱解。利用弱收敛方法得到了一个大偏差原理。证明，避免离散化参数，是基于表示定理，弱收敛和随机最优控制的想法。该方法在相当温和的假设下工作，也适用于由非扩散型的SDES描述的模型。为了说明这一点，我们对待的情况下，时滞的随机微分方程。

Strong and weak convergence for averaging principle of DDSDE with singular drift

In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized $L^p$ spaces. Using Zvonkin's transformation and estimates for solutions to Kolmogorov equations, we prove that the solutions of the original system strongly and weakly converge to the solution of the averaged system as the time scale $\eps$ goes to zero. Moreover, we obtain rates of the strong and weak convergence that depend on $p$ respectively.

A note on the weak rate of convergence for the Euler-Maruyama scheme with Hölder drift

We consider SDEs with bounded and $α$-Hölder continuous drift, with $α\in (0,1)$, driven by multiplicative noise. We show that under sufficient conditions on the diffusion matrix, which guarantee the existence of a unique strong solution, the weak rate of convergence for the Euler-Maruyama scheme is almost $(1+α)/2$. The present paper forms part of the author's master's thesis.

随机积分离散误差过程的Weak convergence与Besov空间

Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces

考虑一类随机积分的Riemann离散所产生的重标误差过程的弱收敛性，并将弱极限的$L_p$ -可积性与随机积分的Malliavin意义下的分数阶光滑性联系起来.

State-discretization of $V$-geometrically ergodic Markov chains and convergence to the stationary distribution

Let $(X_n)_{n \in\mathbb{N}}$ be a $V$-geometrically ergodic Markov chain on a measurable space $\mathbb{X}$ with invariant probability distribution $π$. In this paper, we propose a discretization scheme providing a computable sequence $(\widehatπ_k)_{k\ge 1}$ of probability measures which approximates $π$ as $k$ growths to infinity. The probability measure $\widehatπ_k$ is computed from the invariant probability distribution of a finite Markov chain. The convergence rate in total variation of $(\widehatπ_k)_{k\ge 1}$ to $π$ is given. As a result, the specific case of first order autoregressiv…

卷积概率测度的弱Poincaré不等式

Weak Poincaré Inequality for Convolution Probability Measures

利用李雅普诺夫条件，建立了流形$(M,g)$上某些概率测度的弱Poincaré不等式.这些结果被进一步应用于$\R^d$上的两个概率测度的卷积。随着明确的结果，我们研究具体的例子。

多元部分极大值过程的Weak convergence

Weak convergence of multivariate partial maxima processes

对于严格平稳的$\mathbb{R}_{+}^{d}$ -值随机向量序列，在联合正则变差和弱相依条件下，得到了部分极大值随机过程的泛函收敛性.极限过程是一个极值过程，收敛发生在$[0,1]$上的$\mathbb{R}_{+}^{d}$-值càdlàg函数空间中，具有Skorohod弱$M_{1}$拓扑.我们还表明，这种拓扑结构一般不能被更强的（标准）$M_{1}$拓扑结构所取代。该理论说明了三个例子，包括多元平方Gestival过程与常数条件相关。

关于Harris流的$n$ -点运动的weak convergence的注记

A note on weak convergence of the $n$-point motions of Harris flows

本文将文[2]和[8]中关于光滑Harris流的$n$ -点运动弱收敛到Arratia流的主要结果推广到这些Harris流的协方差函数逐点收敛到一个支持度为零的勒贝格测度的协方差函数的情形。