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

这个项目的目的是调查概率论和统计学领域中选定的近似问题，作为来自德国和圣彼得堡的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和无限维近似及其推广。它们的范围从独立同分布随机变量和向量之和的逼近的经典问题到平稳随机变量和的极大值以及随机过程的按广义Sobolev范数加权的光滑过程的最佳逼近。这在不同的领域都有应用，例如统计学、图像处理和随机矩阵的复数谱的近似中心感兴趣的共同主题是小球概率的控制，其中这一应用的参与者可以受益于德国和俄罗斯研究小组的大量专业知识。

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.