On application of slowly varying functions with remainder in the theory of Markov branching processes with mean one and infinite variance

A. Imomov; A.  Meyliyev

doi:10.37863/umzh.v73i8.684

A. Imomov Karshi State Univ., Uzbekistan
A. Meyliyev Karshi State Univ., Uzbekistan

DOI: https://doi.org/10.37863/umzh.v73i8.684

Keywords: .

Abstract

UDC 519.218.2

We investigate an application of slowly varying functions (in sense of Karamata) in the theory of Markov branching processes. We treat the critical case so that the infinitesimal generating function of the process has the infinite second moment, but it regularly varies with the remainder. We improve the basic lemma of the theory of critical Markov branching processes and refine known limit results.

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