A class of microscopic individual models corresponding to the macroscopic logistic growth. (21st November 2017)

• Record Type: Journal Article
• Authors: Lachowicz, Mirosław
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 8446
• Page End: 8454
• Publication Date: 2017-11-21
• Subjects: asymptotic behavior -- individual‐based models -- logistic equation -- microscopic; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4680
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We study a class of microscopic models corresponding to the standard macroscopic logistic equation. The models at microscale refer to a number of interacting individuals and are in terms of linear evolution equations related to Markov jump processes. The asymptotic large time behavior for the microscopic models is obtained. Moreover, it is shown that any, even nonfactorized, initial probability density tends in the evolution to a factorized equilibrium probability density.