Global solutions to a game-theoretic Riccati equation of stochastic control

In this paper the existence of global solutions to game-theoretic Riccati equations associated to a controlled stochastic differential equation with state dependent white noise is investigated. One proves that if a stabilizing and attenuating feedback exists then a matrix differential game-theoretic Riccati equation of stochastic control has a unique global bounded stabilizing positive semidefinite solution; this solution is periodic if the coefficients are periodic functions and it solves an algebraic Riccati equation if the coefficients are constant. Conversly, if such a solution exists it allows an explicit construction of a stabilizing and disturbance attenuating state feedback. (C) 1997 Academic Press.