### 统计代写|随机过程代写stochastic process代考|MTH7090

statistics-lab™ 为您的留学生涯保驾护航 在代写随机过程stochastic process方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写随机过程stochastic process代写方面经验极为丰富，各种代写随机过程stochastic process相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|随机过程代写stochastic process代考|Matching Theorems

Chapter 4 makes the point that the generic chaining (or some equivalent form of it) is already required to really understand the irregularities occurring in the distribution of $N$ points $\left(X_i\right)_{i \leq N}$ independently and uniformly distributed in the unit square. These irregularities are measured by the “cost” of pairing (=matching) these points with $N$ fixed points that are very uniformly spread, for various notions of cost.
These optimal results involve mysterious powers of $\log N$. We are able to trace them back to the geometry of ellipsoids in Hilbert space, so we start the chapter with an investigation of these ellipsoids in Sect. 4.1. The philosophy of the main result, the ellipsoid theorem, is that an ellipsoid is in some sense somewhat smaller than it appears at first. This is due to convexity: an ellipsoid gets “thinner” when one gets away from its center. The ellipsoid theorem is a special case of a more general result (with the same proof) about the structure of sufficiently convex bodies, one that will have important applications in Chap. 19.

In Sect.4.3, we provide general background on matchings. In Sect.4.5, we investigate the case where the cost of a matching is measured by the average distance between paired points. We prove the result of Ajtai, Komlós and Tusnády that the expected cost of an optimal matching is at most $L \sqrt{\log N} / \sqrt{N}$ where $L$ is a number. The factor $1 / \sqrt{N}$ is simply a scaling factor, but the fractional power of $\log$ is optimal as shown in Sect. 4.6. In Sect. 4.7, we investigate the case where the cost of a matching is measured instead by the maximal distance between paired points. We prove the theorem of Leighton and Shor that the expected cost of a matching is at most $L(\log N)^{3 / 4} / \sqrt{N}$, and the power of $\log$ is shown to be optimal in Sect. 4.8. With the exception of Sect. 4.1, the results of Chap. 4 are not connected to any subsequent material before Chap. 17.

## 统计代写|随机过程代写stochastic process代考|Bernoulli Processes

Random signs are obviously important r.v.s and occur frequently in connection with “symmetrization procedures”, a very useful tool. In a Bernoulli process, the individual random variables $X_t$ are linear combinations of independent random signs. Each Bernoulli process is associated with a Gaussian process in a canonical manner, when one replaces the random signs by independent standard Gaussian r.v.s. The Bernoulli process has better tails than the corresponding Gaussian process (it is “sub-Gaussian”) and is bounded whenever the corresponding Gaussian process is bounded. There is, however, a completely different reason for which a Bernoulli process might be bounded, namely, that the sum of the absolute values of the coefficients of the random signs remain bounded independently of the index $t$. A natural question is then to decide whether these two extreme situations are the only fundamental reasons why a Bernoulli process can be bounded, in the sense that a suitable “mixture” of them occurs in every bounded Bernoulli process. This was the “Bernoulli conjecture” (to be stated formally on page 179), which has been so brilliantly solved by W. Bednorz and R. Latała.

It is a long road to the solution of the Bernoulli conjecture, and we start to build the main tools hearing on Rernoulli processes. A linear combination of independent random signs looks like a Gaussian r.v. when the coefficients of the random signs are small. We can expect that a Bernoulli process will look like a Gaussian process when these coefficients are suitably small. This is a fundamental idea: the key to understanding Rernoulli processes is to reduce to situations where these coefficients are small.

The Bernoulli conjecture, on which the author worked so many years, greatly influenced the way he looked at various processes. In the case of empirical processes, this is explained in Sect. $6.8$.

# 随机过程代考

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。