# A new look to branching Brownian motion from a particle based reaction diffusion dynamics point of view

Source: [A new look to branching Brownian motion from a particle based reaction diffusion dynamics point of view](<https://www.sota2.com/research/paper/68fa5b541e209131ce9c76c5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:00:34.397Z

Authors: Alberto Lanconelli, Berk Tan Per\\c{c}in

Published: 2024-01-19T22:14:00.000Z

## Abstract

Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper \[4\] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles. We derive an infinite system of Fokker-Planck equations that rules the probabilistic evolution of the single particles generated by the branching mechanism and analyse its properties using Malliavin Calculus techniques, following the ideas proposed in \[13\]. Another key ingredient of our approach is the McKean representation for the solution of the Fisher-Kolmogorov-Petrovskii-Piskunov equation and a stochastic counterpart of that equation. We also derive the reaction-diffusion partial differential equation solved by the average concentration field of the branching Brownian system of particles.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2401.11045>)

[PDF](<https://arxiv.org/pdf/2401.11045.pdf>)