We show that several interesting problems in H-infinity-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in [1]. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties, The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns.