Probabilistic approach to a cell growth model

Gregory Derfel, Yaqin Feng, Stanislav Molchanov

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in random proportion between two offsprings (mitosis). Using the technique of moment equations we study asymptotics of the mass distribution of the particles. Mass distribution of the particles is the solution of the equation with linearly transformed argument: functional, functional-differential or integral. We derive several limit theorems describing the fluctuations of the density of the particles, first two moments of the total masses etc.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages95-106
Number of pages12
DOIs
StatePublished - 1 Jan 2019

Publication series

NameContemporary Mathematics
Volume734
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

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