Backbone decomposition of multitype superprocesses

TL;DR

This paper develops a backbone decomposition for multitype supercritical superprocesses, extending known results from one-type cases to multiple types, and also addresses multitype continuous-state branching processes.

Contribution

It introduces the first backbone decomposition for multitype superprocesses, filling a gap in the understanding of their genealogical structure.

Findings

Provides a construction method for the backbone decomposition.

Extends the decomposition to multitype continuous-state branching processes.

Enhances understanding of prolific genealogies in multitype superprocesses.

Abstract

In this paper, we provide a construction of the so-called backbone decomposition for multitype supercritical superprocesses. While backbone decompositions are fairly well-known for both continuous-state branching processes and superprocesses in the one-type case, so far no such decompositions or even description of prolific genealogies have been given for the multitype cases. Here we focus on superprocesses, but by turning the movement off, we get the prolific backbone decomposition for multitype continuous-state branching processes as an easy consequence of our results.