B1387
Title: Martingale method for studying branching random walks
Authors: Elena Yarovaya - Lomonosov Moscow State University (Russia) [presenting]
Abstract: A continuous-time branching random walk is considered on a multidimensional lattice, in which particles can die and produce offspring at any point on the lattice. Let the transport of particles over the lattice be given by a symmetric, homogeneous and irreducible random walk. A branching intensity at a point $x$ at the lattice tends to zero as the norm $|x|$ tends to infinity. Moreover, an additional condition is satisfied for the parameters of the branching random walk, which guarantees exponential growth in the time of the average number of particles at each point of the lattice. Under these assumptions, we prove the limit theorem about the mean square convergence of the normalized number of particles at an arbitrary fixed point $x$, as the time $t$ tends to infinity. The proof is based on the approximation of the normalized number of particles by a nonnegative martingale.
