Contemporary Problems in Probability and Statistics:Gaussian Approximations and Small Deviations for Stochastic Processes

当代概率与统计问题：随机过程的高斯近似和小偏差

• 批准号: 323605340
• 负责人: Professor Dr. Friedrich Götze
• 金额: --
• 依托单位: Laboratory of Algebra and Number Theory Petersburg
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/323605340?language=en
• 关键词: Contemporary; Problems; Probability; Statistics; Gaussian

The aim of this project is to investigate selected approximation problems in the field of probability theory and statistics as a joint effort of research groups from Germany and St. Petersburg. A common feature of all subprojects are Gaussian finite and infinite dimensional approximations and their generalizations. They range from classical problems for the approximation of sums of independent identically distributed random variables and vectors to maxima of sums of stationary random variables and optimal approximation of stochastic processes by classes of smooth processes weighted by generalized Sobolev norms. This has applications in various fields, e.g. statistics, image processing andapproximation of complex spectra of random matrices A common theme of central interest is the control of small ball probabilities where the participants of this application could benefit from the considerable expertise of the research groups in Germany and Russia.

该项目的目的是调查概率论和统计领域的选定近似问题，这是德国和彼得堡研究小组的共同努力。所有子项目的一个共同特征是高斯有限维和无限维近似及其推广。他们的范围从经典问题的近似的总和独立同分布的随机变量和向量的最大值的平稳随机变量和最佳逼近的随机过程的平滑过程加权广义Sobolev规范类的总和。这有应用在各个领域，例如统计，图像处理andapproximation的复杂频谱的随机矩阵的一个共同的主题的中心利益是控制小球的概率，在此应用程序的参与者可以受益于相当大的专业知识的研究小组在德国和俄罗斯。