Abstract.
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.
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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
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Kolokoltsov, V. Measure-valued limits of interacting particle systems with k-nary interactions. Probab. Theory Relat. Fields 126, 364–394 (2003). https://doi.org/10.1007/s00440-003-0267-1
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DOI: https://doi.org/10.1007/s00440-003-0267-1
Keywords
- Markov Process
- Particle System
- Polynomial Growth
- Interact Particle System
- Random Evolution