Multi-valued Stochastic Differential Equations Driven By G-brownian Motion And Related Stochastic Control Problems

In this thesis, we aim to consider a class of multi-valued stochastic differential equations driven by G-Brownian motion(MSDEG in short). This work includes two parts.In the ?rst part, we prove the existence and uniqueness of a solution for the following MSDEG by means of the Yosida approximation methodwhere B· is a G-Brownian motion, B · is the quadratic variation process associated with B·, ?? is the subdifferential operator associated to , which is a lower and semicontinuous(l.s.c., in short) function on Rd.In the second part, we consider the optimal control problem associated to the above MSDEG We set up an optimality principle of stochastic control problem, i.e., the dynamic programming principle. Then, we prove the value function of the control problem is the unique viscosity solution of a class of second order parabolic differential equations involving a multi-valued operator.