This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving large number weakly-coupled interactive agents under generalized setting. For each individual agent, the control and state process enters both diffusion drift terms in its linear dynamics, weight might be indefinite cost functional. setup is innovative has great theoretical rea...

In this note we effect a reduction of the theory of hermitian forms of two particular types (coefficients in a quadratic field or in a quaternion algebra with the usual anti-automorphism) to that of quadratic forms. The main theorem (§2) enables us to apply directly the known results on quadratic forms. This is illustrated in the discussion in §3 of a number of special cases. Let <£ be an arbit...