Convergence of a jump procedure in a semi-Markov environment in diffusion-approximation scheme. (English. Russian original) Zbl 1255.60159
Cybern. Syst. Anal. 43, No. 6, 866-875 (2007); translation from Kibern. Sist. Anal. 2007, No. 6, 124-133 (2007).
Summary: The sufficient convergence conditions are obtained for a jump stochastic approximation procedure in a semi-Markov environment in a diffusion approximation scheme with balance conditions for a singular perturbation of the regression function. To this end, a singular perturbation problem is solved for the asymptotic representation of the compensating operator of an augmented Markov renewal process.
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