Discrete Feynman-Kac formulas for branching random walks

Details Discrete Feynman-Kac formulas for branching random walks Discrete Feynman-Kac formulas for branching random walks

2012-02-13

arxiv.org/abs/1202.2811v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

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.

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