Asymptotic Behavior of Constrained Stochastic Approximations via the Theory of Large Deviations

摘要

This paper is organized as follows. In section 2, various terms from the theory of large deviations are introduced, and the problem (on a time interval O,T) formulated. Sections 3 and 4 contain some technical results concerning the action functional and approximations of (1.1). These are put together in section 5 to get the general large deviations result. Section 6 concerns the mean escape time of (1.1) from a neighborhood of a stable point of (1.2) and in section 7 we remark on some extensions to the global behavior of (1.1) on the infinite time interval O, infinity, the character of movement from stable point to stable point and on the stochastic approximation case.