# A low-rank technique for computing the quasi-stationary distribution of subcritical Galton-Watson processes

## TL;DR

This paper introduces a novel low-rank algorithm for efficiently computing the quasi-stationary distribution of subcritical Galton-Watson processes, extending to multitype cases, with demonstrated accuracy and efficiency improvements.

## Contribution

The paper presents a new low-rank discretization method for the quasi-stationary distribution, including theoretical analysis and extension to multitype processes.

## Key findings

- Algorithm is more accurate than existing methods.
- Algorithm is more efficient computationally.
- Effective extension to multitype branching processes.

## Abstract

We present a new algorithm for computing the quasi-stationary distribution of subcritical Galton--Watson branching processes. This algorithm is based on a particular discretization of a well-known functional equation that characterizes the quasi-stationary distribution of these processes. We provide a theoretical analysis of the approximate low-rank structure that stems from this discretization, and we extend the procedure to multitype branching processes. We use numerical examples to demonstrate that our algorithm is both more accurate and more efficient than other approaches.