Report title: the Operator - valued, backward stochastic Riccati equations and application

Reporter: professor zhang xu, sichuan university

Report time: 10:00-11:00 am, November 7, 2019

Location: 2nd lecture hall, mathematics building

Summary of report:

We introduce an operator - valued, backward stochastic Riccati equation for a general stochastic linear quadratic control problem in infinite dimensions. Generally speaking, The well - posedness of this equation is a challenging problem. Indeed, in the infinite dimensional setting, There exists no satisfactory stochastic integration/evolution equation and found () in the literatures which can be employed to treat the well - posedness of to a quadratically nonlinear equation. The to Overcome this difficulty, we adapt our transposition solution method, which was developed in our previous works but for operator-valued, Backward stochastic (linear) Lyapunov equations, Under some assumptions. We establish the equivalence between the existence of optimal feedback operator for infinite dimensional stochastic linear quadratic control the problems with random coefficients and the solvability of The corresponding operator - valued, backward stochastic Riccati equations.

About the speaker:

Professor zhang xu, professor of sichuan university, winner of the national outstanding youth fund, selected member of the "hundred talents program" of the Chinese Academy of Sciences, distinguished professor of "cheungkong scholars" of the Ministry of Education. Professor zhang xu's main research area is mathematical cybernetics and related partial differential equations and stochastic analysis. He has won the second prize of national natural science. He has been the editorial board and deputy editor of two major international journals in his research field, SIAM j. Control Optim., ESAIM Control optim. calc. Var., Acta appl. Math. Member of the editorial board of math.control relat.fields.