Discrete Feynman-Kac formulas for branching random walks

Abstract

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.

4 pages, 3 figures

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• Killing versus branching: Unexplored facets of diffusive relaxation
• Tamed Feynman-Kac diffusion processes: Killing-branching intertwine