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

• Applicant: Professor Dr. Friedrich Götze
• Subject Area: Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 323605340

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.

• DFG Programme: Research Grants
• International Connection: Russia
• Co-Investigators: Professor Dr. Frank Aurzada; Professor Dr. Steffen Dereich; Professor Dr. Zakhar Kabluchko; Professor Dr. Holger Kösters
• Cooperation Partners: Professor Dr. Andrei Borodin; Professor Dr. Alexey Andreevich Karthov; Professor Dr. Mikhail Lifshits; Professor Dr. Alexander I. Nazarov; Professor Dr. Yakov Nikitin; Professor Dr. Ruslan Pusev; Dr. Nikita Rastegaev; Professorin Dr. Ksenia Volkova; Professor Dr. Andrei Yaitsev; Professor Dr. Andrei Zaitsev