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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.

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References

  1. D. A. Dawson, “Measure-valued Markov processes. Ecole d’Ete de Probabilities de Saint Flour, 1991,” Lect. Notes. Math., 1541, 260 (1993).

    Google Scholar 

  2. E. B. Dynkin, An Introduction to Branching Measure-Valued Processes, AMS, Providence, Rhode Island (1994).

    MATH  Google Scholar 

  3. A. V. Skorokhod, Stochastic Equations for Complex Systems, Riedel, Dordrecht (1988).

    MATH  Google Scholar 

  4. P. Kotelenez, “A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation” Probab. Theory Related Fields, 102, 159–188 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Ya. Maydaniuk and A. V. Skorokhod, “Quasi-diffusion measure-valued processes and a limit theorem for jump measure-valued Markov processes,” in: Exploring Stochastic Laws. Festschrift in Honour of the 70th Birthday of V. S. Korolyuk, Utrecht, The Netherlands (1995), pp. 275–284.

  6. M. I. Freidlin, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, New Jersey (1985).

    MATH  Google Scholar 

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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

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