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 nV 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.
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