2017
Том 69
№ 9

All Issues

Asymptotic normality of fluctuations of the procedure of stochastic approximation with diffusive perturbation in a Markov medium

Chabanyuk Ya. M.

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Abstract

We consider the asymptotic normality of a continuous procedure of stochastic approximation in the case where the regression function contains a singularly perturbed term depending on the external medium described by a uniformly ergodic Markov process. Within the framework of the scheme of diffusion approximation, we formulate sufficient conditions for asymptotic normality in terms of the existence of a Lyapunov function for the corresponding averaged equation.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 12, pp 1916-1923.

Citation Example: Chabanyuk Ya. M. Asymptotic normality of fluctuations of the procedure of stochastic approximation with diffusive perturbation in a Markov medium // Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1686–1692.

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