Residence times of branching diffusion processes
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Updated: Mar 15, 2026

Molecular Diffusion in Plasma Membranes of Primary Lymphocytes Measured by Fluorescence Correlation Spectroscopy
Published on: February 1, 2017
1IRSN, Nuclear Safety Division, 31 Avenue de la Division Leclerc, 92260 Fontenay-aux-Roses, France.
Abstract:
The residence time of a branching Brownian process is the amount of time that the mother particle and all its descendants spend inside a domain. Using the Feynman-Kac formalism, we derive the residence-time equation as well as the equations for its moments for a branching diffusion process with an arbitrary number of descendants. This general approach is illustrated with simple examples in free space and in confined geometries where explicit formulas for the moments are obtained within the long time limit. In particular, we study in detail the influence of the branching mechanism on those moments. The present approach can also be applied to investigate other additive functionals of branching Brownian process.
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