On a general kinetic equation for many–particle systems with interaction, fragmentation and coagulation

Abstract
We deduce the most general nonlinear kinetic equation that describes the low–density limit of general Feller processes for systems of random numbers of classical particles with interaction, collisions, fragmentation and coagulation. This is done by studying the limiting (as ∈ → 0) evolution of Feller processes on ∪∞n=0 Xn with X = Rd or X = Zd described by generators of the form ∈–1∑k=0k ∈kB(k), K ∈ N, where B(k) are the generators of k–nary interaction, whose general structure is also described in this paper.