A1437
Title: Spectral methods and their application in stochastic analysis
Authors: Elena Yarovaya - Lomonosov Moscow State University (Russia) [presenting]
Abstract: The development of spectral technique allows obtaining limit theorems on the numbers of particles in a branching random walk on points of a multidimensional lattice under the assumption of the existence of branching sources (i.e., lattice points, in which particles can multiply and die) with both positive and negative branching intensities. The results on the relationship between the structure of the evolution operator spectrum and the geometric location of branching sources on a multidimensional lattice will be presented. As a rule, in earlier studies, the underlying random walk was assumed to be symmetric. It is shown that the obtained results remain valid when the condition of self-adjointness of the operator defining the random walk to a weaker condition of similarity to the self-adjoint one. Thus, with the use of spectral techniques, problems are solved related to multipoint perturbations of operators arising in the evolution equations for the first moments of particle numbers in multitype branching random walks and proved a number of new limit theorems on the behavior of populations and subpopulations of particles in a branching random walk.
