On asymptotic structure of continuous-time Markov Branching Processes allowing Immigration and without high-order moments

TL;DR

This paper investigates the long-term behavior of continuous-time Markov Branching Processes with immigration, focusing on cases lacking high-order moments and using advanced mathematical tools to analyze their convergence properties.

Contribution

It introduces new limit theorems for these processes using regularly varying generating functions, expanding understanding of their asymptotic structure without requiring high-order moments.

Findings

Transition functions converge to invariant measures

Limit properties are characterized using regularly varying functions

Results apply to processes without high-order moments

Abstract

We observe the continuous-time Markov Branching Process without high-order moments and allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. Main mathematical tool is regularly varying generating functions with remainder.