Project Details
Projekt
A unified approach to limit theorems for dual objects in probabilita and number theory
Subject Area
Mathematics
Term
from 2016 to 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 289386657
The aim of this project is to extend the general approach developed in the monograph by V. V. Buldygin, K.-H. Indlekofer, O. I. Klesov, and J. G. Steinebach on "Pseudo-Regularly Varying Functions and Generalized Renewal Processes" (TBiMC, Kyiv, 2012) to study the rate of convergence in limit theorems for various dual objects.Via a unified point of view from the analysis of real functions and sequences, our approach is to derive several equivalencies of asymptotic statements in probability theory as well as in number theory and to develop similar results for other fields of interest.For example, relationships between the Marcinkiewicz-Zygmund type strong laws of large numbers or laws of the iterated logarithm for sums of independent random variables and their corresponding renewal processes are specific results from probability theory included in the topics of this project.Similarly, limiting distributions and rates of convergence for multiplicative and additive functions in number theory and their extensions are a further example of applications. Another challenging problem of the project is to discover possible counterparts of number theoretical results in probability theory, looking very similar to the above mentioned results in renewal theory.Our general approach is based on the theory of pseudo-regularly varying functions, taking advantage of their specific properties which allow to draw very general asymptotic conclusions. The further development of such classes of functions will also be investigated in order to extend the results to a wide area of applications.
DFG Programme
Research Grants
International Connection
Hungary, Ukraine
Cooperation Partner
Professor Dr. Imre Katai
International Co-Applicant
Professor Dr. Oleg I. Klesov
