Skorokhod, A. V. 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. Reviewer: A.N.Kochubei (Kyïv) Cited in 3 ReviewsCited in 1 Document MSC: 60J25 Continuous-time Markov processes on general state spaces 60G57 Random measures Keywords:diffusion; Markov process; measure-valued process; semimartingale; randomly interacting particles PDFBibTeX XMLCite \textit{A. V. Skorokhod}, Ukr. Mat. Zh. 49, No. 3, 458--464 (1997; Zbl 0943.60065) Full Text: DOI