Simulation of Branching Random Walks on a Multidimensional Lattice

Abstract

We consider continuous-time branching random walks on multidimensional lattices with birth and death of particles at a finite number of lattice points. Such processes are used in numerous applications, in particular, in statistical physics, population dynamics, and chemical kinetics. In the last decade, for various models of branching random walks, a series of limit theorems about the behavior of the process for large times has been obtained. However, it is almost impossible to analyze analytically branching random walks on finite time intervals; so in this paper we present an algorithm for simulating branching random walks and examples of its numerical realization.