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