Oleg Klesov: Pseudo-regularly varying functions and some applications

Abstract:

The notion of pseudo-regularly varying (PRV) functions is a generalization of the notion of regularly varying (RV) functions. PRV functions keep only those properties of RV functions that are necessary to study their limit behavior.

Some motivations for introducing such a notion is discussed in the talk as well as some known applications in number theory, mathematical analysis, theory of ordinary differential equations, stochastic differential equations and limit theorems of probability theory (especially in the theory of renewal processes).

The talk is based on joint research works with Valerii Buldygin, Karl-Heinz Indlekofer, and Josef Steinebach. Some of them are reflected in the joint monograph "Pseudo-Regularly Varying Functions and Generalized Renewal Processes", Springer, Cham, 2018.