In a major breakthrough, Guo and Chen [1] have recently shown how to establish the self-optimality and mean square stability of a self-tuning regulator. The ideas there allow us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering, control and identification. In adaptive filtering, we examine both indirect and noninterlaced direct schemes for prediction, using both least-squares and gradient parameter estimation algorithms. In addition to analyzing similar direct adaptive control algorithms, we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection. We also establish that the parameters converge to the null space of a certain matrix. From this one may deduce the convergence of several adaptive controllers.