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Bibliographic Details
Main Authors: Lanconelli, Alberto, Perçin, Berk Tan
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.11045
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Table of Contents:
  • 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.