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arXiv · 1202.2811

Discrete Feynman-Kac formulas for branching random walks

Andrea Zoia·Eric Dumonteil·Alain Mazzolo
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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.

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Andrea Zoia, Eric Dumonteil, Alain Mazzolo. 2012-02-13. Discrete Feynman-Kac formulas for branching random walks. https://doi.org/10.1209/0295-5075%2F98%2F40012

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