Abstract
We consider a new class of Markov processes in the space of measures with constant mass. We present the construction of such processes in terms of probabilities that control the motion of individual particles. We study additive functionals of such processes and give examples related to stochastic flows with interaction.
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REFERENCES
A. V. Skorokhod, Random Linear Operators [in Russian], Naukova Dumka, Kiev (1979).
A. A. Dorogovtsev and P. Kotelenez, Smooth Stationary Solutions of Quasilinear Stochastic Partial Differential Equations:1. Finite Mass, Preprint No. 97-145, Cleveland (1997).
A. A. Dorogovtsev, “Stochastic flows and random measure-valued processes in abstract space,” in: Abstracts of the International Conference “Stochastic Analysis and Its Applications” (Lviv, June 10-17, 2001), Lviv (2001), p. 15.
E. B. Dynkin, Markov Processes [in Russian], Fizmatgiz, Moscow (1963).
A. A. Dorogovtsev and N. Yu. Goncharuk, Local Times for Measure-Valued Ito's Stochastic Processes, Preprint No. 95-142, Cleveland (1995).
N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland, Amsterdam (1981).
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Dorogovtsev, A.A. Measure-Valued Markov Processes and Stochastic Flows. Ukrainian Mathematical Journal 54, 218–232 (2002). https://doi.org/10.1023/A:1020182428332
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DOI: https://doi.org/10.1023/A:1020182428332