Discrete Feynman-Kac formulas for branching random walks

Andrea Zoia, Eric Dumonteil, Alain Mazzolo

Published 2012-02-13Version 1

Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete Feynman-Kac equations for the probability and the moments of the number of visits $n_V$ of the walker to a given region $V$ in the phase space. Feynman-Kac formulas for the residence times of Markovian processes are recovered in the diffusion limit.