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

  • Ya. M. Chabanyuk

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.
Published
25.12.2006
How to Cite
Chabanyuk, Y. M. “Asymptotic Normality of Fluctuations of the Procedure of Stochastic Approximation With Diffusive Perturbation in a Markov Medium”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 12, Dec. 2006, pp. 1686–1692, http://umj.imath.kiev.ua/index.php/umj/article/view/3564.
Section
Research articles