Weak convergence conditions are obtained for a diffusion transfer process with Markov switchings and a control with an equilibrium point of quality criterion functions. A procedure is constructed for the stochastic approximation of such a point in a scheme of series.
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I. I. Gikhman and A. V. Skorokhod, Controlled Random Processes [in Russian], Naukova Dumka, Kiev (1977).
J. Jacod and A. N. Shiryaev, Limit theorems for Random Processes [Russian translation], Vol. 1, Fizmatgiz, Moscow (1994).
M. B. Nevelson and R. Z. Khasminskii, Stochastic Approximation and Recursive Estimation [in Russian], Nauka, Moscow (1972).
V. B. Kolmanovskii, “Problems of optimal estimation,” Soros Educational Journal, No. 11, 122–127 (1999).
A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1987).
V. S. Korolyuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific, London–Singapore-Hong Kong (2005).
V. S. Korolyuk, Stochastic Models of Systems [in Ukrainian], Naukova Dumka, Kyiv (1989).
U. T. Khimka and Ya. M. Chabanyuk, “A difference stochastic optimization procedure with impulse perturbation,” Cybernetics and Systems Analysis, 49, No. 3, 768–773 (2013).
Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 169–175, July–August, 2015.
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Nikitin, A.V. Asymptotic Properties of a Stochastic Diffusion Transfer Process with an Equilibrium Point of a Quality Criterion. Cybern Syst Anal 51, 650–656 (2015). https://doi.org/10.1007/s10559-015-9756-3
- stochastic diffusion equation
- generator on a Banach space
- Markov process
- stochastic approximation procedure