Mesoscopic description of individual based models: how to reduce the losses.
Abstract: We consider a unified approach to different mesoscopic scalings for a wide class of generators for individual-based models. The generators describe eventual (and density dependent) changes of complex systems, when a group of elements may change their positions and/or threats, or just disappear whereas a new group may appear in the phase space. The properly rescaled dynamics of the corresponding correlation functions allows to find a (nonlinear) equation which describes an approximate mesoscopic density of the system. We show also how to find the next term of the expansion of the real mesoscopic density in scaling parameter to reduce the error term. To do this, we present a nonlinear hierarchy which describes the time-evolution of the cummulants for the considered dynamics.