Kinetic Equations for the Pure Jump Models of k-nary Interacting Particle Systems

V.N. Kolokol'tsov

2006, v.12, Issue 1, 95-138


The dynamic law of large numbers of k-nary interacting particles is described by nonlinear measure-valued equations that generalize the classical kinetic equations of statistical mechanics and the evolutionary (replicator) dynamics from population biology and evolutionary games. Rigorous results on convergence, existence and uniqueness theorems for the limiting equations, and the propagation of chaos property are established for models with interactions of pure jump type.

Keywords: interacting particles,k-nary interaction,measure-valuedlimits,kinetic equation,mean-field limit,mass exchange processes,coagulation-fragmentation,propagation of chaos,evolutionary games,replicator dynamics


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