# Approximation of the Height process of a CSBP with interaction

## TL;DR

This paper demonstrates that the rescaled height process of genealogical trees in continuous time branching processes converges to a limit, extending the results to generalized processes with interaction, thus advancing understanding of their genealogical structures.

## Contribution

It introduces convergence results for the height process of genealogical trees in both classical and generalized branching processes with interaction.

## Key findings

- Rescaled height process converges to the height process of a CSBP
- Extension of convergence results to processes with interaction
- Provides a unified framework for genealogical convergence in branching processes

## Abstract

In this work, we first show that the properly rescaled height process of the genealogical tree of a continuous time branching process converges to the height process of the genealogy of a (possibly discontinuous) continuous state branching process. We then prove the same type of result for generalized branching processes with interaction.