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

该项目的目的是研究概率论和统计学领域的选定近似问题，作为德国和圣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。它们的范围从独立的同分布随机变量和向量的和的近似的经典问题，到平稳随机变量和的和的最大值，以及由广义Sobolev范数加权的光滑过程类的随机过程的最优近似。这在各个领域都有应用，例如统计，图像处理和随机矩阵复杂光谱的近似。一个共同的主题是小球概率的控制，这个应用的参与者可以从德国和俄罗斯的研究小组的大量专业知识中受益。

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.