Steady state for the subcritical contact branching random walk on the lattice with the arbitrary number of offspring and with immigration

TL;DR

This paper proves the existence of a steady state for a subcritical contact branching random walk on a lattice, incorporating arbitrary offspring numbers and immigration, contributing to understanding long-term behavior in such stochastic processes.

Contribution

It establishes the existence of a steady state for the subcritical contact branching random walk with arbitrary offspring and immigration, a novel result in this context.

Findings

Existence of a steady state in the process.

Applicable to arbitrary offspring numbers.

Incorporates immigration in the model.

Abstract

We consider the subcritical contact branching random walk on Zd in continuous time with the arbitrary number of offspring and with immigration. We prove the existence of the steady state (statistical equilibrium).