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

References in corpus (4)

• First-passage times in complex scale-invariant media
• The survival probability of a branching random walk in presence of an absorbing wall
• Neutral Evolution as Diffusion in phenotype space: reproduction with mutation but without selection
• Collision number statistics for transport processes

Cited by in corpus (3)

• Properties of branching exponential flights in bounded domains
• Branching exponential flights: travelled lengths and collision statistics
• Cauchy's formulas for random walks in bounded domains