Some limit theorems for flows of branching processes

TL;DR

This paper develops limit theorems for flows of Galton-Watson branching processes, showing how they converge to continuous superprocesses, thus advancing understanding of their asymptotic behavior.

Contribution

It introduces new scaling limit theorems for stochastic flows of branching processes, connecting discrete models to continuous superprocesses.

Findings

Proved local and nonlocal branching superprocesses as limits

Established convergence of discrete flows to continuous processes

Enhanced understanding of branching process asymptotics

Abstract

We construct two kinds of stochastic flows of discrete Galton-Watson branching processes. Some scaling limit theorems for the flows are proved, which lead to local and nonlocal branching superprocesses over the positive half line.