Measure-valued limits of interacting particle systems with <Emphasis Type="Italic">k</Emphasis>-nary interactions

 Results on existence, uniqueness, non-explosion and stochastic monotonicity are obtained for one-dimensional Markov processes having non-local pseudo-differential generators with symbols of polynomial growth. It is proven that the processes of this kind can be obtained as the limits of random evolutions of systems of identical indistinguishable particles with k-nary interaction. Received: 24 May 2002 / Revised version: 19 February 2003 / Published online: 12 May 2003 Mathematics Subject Classification (2000): 60K35, 60J75, 60J80 Key words or phrases: Interacting particles – k-nary interaction – Measure-valued processes – One-dimensional Feller processes with polynomially growing symbols – Duality – Stochastic monotonicity – Heat kernel