# On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration

## TL;DR

This paper investigates the long-term behavior of critical Galton-Watson branching processes with infinite variance and immigration, focusing on their transition functions and convergence to invariant measures.

## Contribution

It provides new insights into the asymptotic structure and limit properties of such processes with infinite variance and immigration.

## Key findings

- Convergence of transition functions to invariant measures
- Characterization of asymptotic behavior in infinite variance cases
- Extension of classical results to processes with immigration

## Abstract

We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.