Title: Branching random walks: Theoretical and simulation results
Authors: Elena Yarovaya - Lomonosov Moscow State University (Russia) [presenting]
Abstract: The focus is on various models of a continuous-time process with generation and walking of particles on multidimensional lattices. Points of the lattice, at which the particle generation, that is birth and death of particles, can occur, are called sources of branching, and the process itself is called a branching random walk (BRW). A series of asymptotic results are provided on the behavior of the particle numbers and/or their integer moments for the following models: 1) a symmetric BRW with one source of branching and a finite or infinite number of the initial particles; 2) a symmetric BRW with a finite number of sources of various positive intensities and one initial particle; 3) a BRW with pseudo-sources, admitting possible violation of symmetry of an underlying random walk at sources of branching and one initial particle; 4) a BRW with sources at every lattice point, in which the reproduction law is described by a critical Bienamye-Galton-Watson process, and infinite number of the initial particles. In addition to the limit theorems, the simulations results based on the Monte Carlo method is represented.