In this talk, I will present my work (jointly with Qi Lü) on characterization of optimal feedback for stochastic linear quadratic control in infinite dimensions by means of Riccati type equations. More precisely, under some assumptions which can be verified for interesting concrete models, we establish the equivalence between the existence of optimal feedback operator for infinite dimensional stochastic linear quadratic control problems and the solvability of the corresponding operator-valued, backward stochastic Riccati equations. In order to handle the latter nonlinear equations, we adapt our stochastic transposition method, which was developed in our previous works but for operator-valued, backward stochastic (linear) Lyapunov equations.
张旭,四川大学教授,教育部长江学者特聘教授,国家杰出青年科学基金获得者。独立获得国家自然科学二等奖、教育部自然科学一等奖。应邀在国际数学家大会作45分钟学术报告。