This article is cited in 2 papers

Harmonic analysis of random walks with heavy tails

A. I. Rytova

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider a continuous-time symmetric, spatially homogeneous branching random walk on a multidimensional lattice with a single branching source. Corresponding transition intensities of the underlying random walk are assumed to have heavy tails. This assumption implies that the variance of jumps is infinite. The growth rate estimate of the Fourier transform for transition intensities and of the asymptotics of the mean number of particles in the source in subcritical case are obtained.

UDC: 519.21

 English version: Journal of Mathematical Sciences (New York), 2022, 262:4, 514–524