Interactions between resource dependent branching processes and equilibria

TL;DR

This paper provides detailed proofs and supplementary comments on resource-dependent branching processes and their equilibria, extending prior work on human population dynamics and optimal transport in an econometric context.

Contribution

It offers rigorous proofs and practical insights complementing previous research on population-resource interactions and equilibrium analysis.

Findings

Proofs of key theorems on resource-dependent branching processes

Comments on control and optimal stopping problems in population management

Enhanced understanding of equilibria in resource-dependent models

Abstract

This paper is a supplement to the paper "Interactions between Human Populations and Related Problems of Optimal Transport" written by the same author in honour of Marc Hallin, Universit\'e Libre de Bruxelles, at the occasion of Hallin's $75$th birthday. It was announced in the main paper (Bruss (2024)) published in the Springer Festschrift entitled {\it Recent Advances in Econometrics and Statistics}. It contains the proofs which, given the space constraints required for the Festschrift, could not appear in the main paper. Moreover, we complement in the present supplement the main paper by brief comments on related problems which are likely to turn up in practice for problems of guiding human populations, namely problems of control and problems of optimal stopping.