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Measure-valued diffusion. (English) Zbl 0943.60065

Ukr. Math. J. 49, No. 3, 506-513 (1997) and Ukr. Mat. Zh. 49, No. 3, 458-464 (1997).
The author considers the class of continuous measure-valued processes \(\{ \mu_t\}\) on a finite-dimensional Euclidean space \(X\) for which \(\int f d\mu_t\) is a semimartingale with an absolutely continuous characteristic (with respect to \(t\)) for any smooth \(f:\;X\to \mathbb{R}\). It is shown that under certain general conditions a Markov process with this property can be obtained as a weak limit of systems of randomly interacting particles which move in \(X\) along the trajectories of a diffusion on \(X\) as the number of particles increases to infinity.

MSC:

60J25 Continuous-time Markov processes on general state spaces
60G57 Random measures
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