variable Y = Y(xl, X2, * **, Xk) depending on k real valued parameters xl, X2, Xk, , determine the values of these parameters which minimize

by making a sequence of independent observations of the random variable Y at different values of the parameters. In the field of communications we are usually more interested in the case in which Y is an ergodic random process Yt. Here we consider this situation and study a continuous version of the KieferWolfowitz procedure. The advantage of using a continuous version of the procedure when Yt is a continuous time-parameter process (as opposed to periodically sampling Yt and applying the original procedure to the samples) lies in the fact that it may be mechanized with simple analog computation components. Our analysis considers a straightforward generalization of the original procedure and, to a certain extent, follows the pattern of Dupa6's analysis [6] of the original procedure. The hypotheses of the theorems which we present are chosen from the standpoint of applicability to certain communication and data processing problems rather than from the standpoint of mathematical generality. Other continuous stochastic approximation methods have received treatment [4], [5], [7], but none seem appropriate for data processing applications. For the one-dimensional case Drirnl and Nedoma [5] consider a continuous version of a generalized Robbins-Munro procedure and obtain almost sure convergence under more liberal assumptions than are made here: unfortunately, their analysis cannot be extended to the multidimensional case. Neither of the procedures considered by Driml and Hang [4] and Hang and Spa6ek [7] seem particularly well suited for analog computation. 2. Notation and description of the approximation procedure. We regard the k parameters xl, X2, ... Xk as the components of a k-dimensional vector x. The basis for the space will be the unit vectors el, e2, ... ek, ei denoting a unit value of xi and zero values for the other k - 1 parameters. We will denote the usual Euclidean norm and inner product by lixII and (x, y) respectively. We