Riccati Differential and Algebraic Equations from Stochastic Differential Games
Michael J. McAsey, Libin Mou · 2002
In this paper we study a class of matrix differential and algebraic Riccati equations arising from stochastic differential games with a quadratic cost. We will use the notion of upper and lower solutions to give necessary and sufficient conditions for the existence of solutions to the equations. We also obtain a monotonicity, a comparison theorem and interpretation theorems for upper and lower solutions. In addition, the mean-square stability of solutions is also discussed. §