Abstract
We consider the problem of random mass transfer on a metric compactum defined by a purely discontinuous stochastic semigroup \(T_t^s\). We give a description of this semigroup based on a Markov process with random transition probability. We present conditions for the independence of measure-valued processes of the form \(T_t^0 {\mu}_{0}\), depending on the initial mass μ0.
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REFERENCES
H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge (1990).
R. W. R. Darling, “Ergodicity of measure-valued Markov chain induced by random transformations,” Probab. Th. Rel. Fields., 77, 221–229 (1998).
A. V. Skorokhod, Random Linear Operators [in Russian], Naukova Dumka, Kiev (1978).
A. V. Skorokhod, Lectures on the Theory of Random Processes [in Ukrainian], Lybid', Kiev (1990).
G. Lu and A. Mukherjea, “Invariant measures and Markov chains with random transition probabilities,” Probab. Math. Statist., 2, 115–138 (1997).
T. Liggett, Interacting Particle Systems, Springer, Berlin (1985).
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Feshchenko, O.Y. Stochastic Semigroups and Random Mass Transfer. Ukrainian Mathematical Journal 53, 1507–1518 (2001). https://doi.org/10.1023/A:1014370825931
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DOI: https://doi.org/10.1023/A:1014370825931