Fluctuations of a stochastic approximation procedure with diffusion perturbation

A stochastic approximation procedure with a singularly perturbed regression function is considered. The form of the limit process is obtained that corresponds to the fluctuation of the stochastic approximation procedure in the neighborhood of an equilibrium point. A generator for the limit process is also constructed. The solution of the singular perturbation problem is given for the asymptotic representation of the generator of a Markov renewal process. The results obtained allow one to extend the possibilities of investigation of the asymptotic behavior of the procedure itself.