Abstract
We consider the class of continuous measure-valued processes {μ t } on a finite-dimensional Euclidean space X for which ∫fd μ t is a semimartingale with absolutely continuous characteristics with respect to t for all f:X→R smooth enough. It is shown that, under some general condition, the Markov process with this property can be obtained as a weak limit for systems of randomly interacting particles that are moving in X along the trajectories of a diffusion process in X as the number of particles increases to infinity.
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Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev; Michigan University, Michigan. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 458–464, March, 1997.
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Skorokhod, A.V. Measure-valued diffusion. Ukr Math J 49, 506–513 (1997). https://doi.org/10.1007/BF02487246
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DOI: https://doi.org/10.1007/BF02487246