It is shown that Markov chains in Zd þ describing k-nary interacting particles of d different types approximate (in the continuous state limit) Markov processes on Rd þ having pseudo-differential generators p ðx; ið›=›xÞÞ with symbols p (x,j) depending polynomially (degree k) onx. This approximation can be used to prove existence and nonexplosion results for the latter processes. Our general scheme of continuous state (or finite-dimensional measurevalued) limits to processes of k-nary interaction yields a unified description of these limits for a large variety of models that are intensively studied in different domains of natural science from interacting particles in statistical mechanics (e.g. coagulation-fragmentation processes) to evolutionary games and multidimensional birth and death processes from biology and social sciences
