2017
Том 69
№ 9

All Issues

Measure-valued diffusion

Skorokhod A. V.

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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.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 3, pp 506-513.

Citation Example: Skorokhod A. V. Measure-valued diffusion // Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 458–464.

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