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The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.
Let be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.
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