A local maximal inequality under uniform entropy

A note on a maximal Bernstein inequality

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces

In this paper we generalize the Hájek-Rényi-Chow maximal inequality for submartingales to $L^p$ type Riesz spaces with conditional expectation operators. As applications we obtain a submartingale convergence theorem and a strong law of large numbers in Riesz spaces. Along the way we develop a Riesz space variant of the Clarkson's inequality for $1\le p\le 2$.

A stochastic maximal inequality, strict countability, and related topics

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using Itô's formula and on a new concept named strict countability, is presented. The main results are some weak convergence theorems for sequences of separable random fields of locally square-integrable martingales under the uniform topology with the help also of entropy methods. As special cases, some new results for i.i.d. random sequences, including a new Donsker theorem and a moment bou…

$\mathcal{L}_{q}$-极大不等式：相依高维均值

$\mathcal{L}_{q}$-maximal inequality for high dimensional means under dependence

本文针对高维相依随机变量推导$\mathcal{L}_{q}$-极大不等式，上界含$\ln(p)$与Kolmogorov距离，并在混合与物理相依条件下证明其趋于零。

弱相依条件下局部经验过程的一个极大不等式

A maximal inequality for local empirical processes under weak dependence

本文针对强混合数据下的局部经验过程建立了一个非渐近极大不等式，该不等式在函数类、取值点和带宽上一致控制估计误差，并应用于核密度估计，证明在弱相依条件下可获得与独立同分布情形几乎相同的尖锐一致带宽速率。

可分交换经验过程的最大不等式

Maximal Inequalities for Separately Exchangeable Empirical Processes

本文针对可分交换随机阵列的经验过程，通过将指标集划分为横截组以解耦相依性，建立了全局与局部最大不等式，分别控制上确界的高阶矩和一阶绝对矩。