On the Generating Functional of the special case of S-Stopped Branching Processes

TL;DR

This paper investigates the generating functional of a stopped branching process with infinitely many particle types, where the process halts upon reaching a specific non-empty set, providing insights into its probabilistic structure.

Contribution

It introduces the generating functional for a special stopped branching process with infinitely many types, extending existing theory to this complex case.

Findings

Derived the generating functional for the stopped process.

Analyzed the process's behavior upon reaching set S.

Extended branching process theory to infinite types case.

Abstract

In this paper starting process with the infinite number of types of particles \mu(t) generate stopped branching process \xi(t), if by falling of the first one into the non empty set S process stops. Here we consider the generating functional of the upper defined process.