Simulation of processes in a random environment

On a multidimensional lattice we consider continuous-time branching random walks with multiplication and death of particles in a finite number of selected nodes. Such processes are used in numerous applications, in particular, in statistical physics, population dynamics, chemical kinetics. In the last decade, a number of limit theorems on the behavior of the process at large times have been obtained for various models of branching random walks. However, the study of branching random walks is practically impossible to perform analytically on finite time intervals, so this paper will present an algorithm for modeling branching random walks and examples of its numerical implementation.