Averaging Method for Stochastic Approximations with Constant Parameters: Small Parameter Values

摘要

Stochastic approximations with constant gain coefficients and dependent noise and nonlinear or even discontinuous dynamics have many applications in control, automata and communication theory. When the gain coefficient is small, an asymptotic theory is developed which gives much information on the character of the paths and errors. The method involves both averaging and stability ideas. The ideas are outlined. An example which illustrates the basic ideas and techniques is given. (KR)