A class of microscopic individual models corresponding to the macroscopic logistic growth.

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. [ABSTRACT FROM AUTHOR]