A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H_2/H_∞ CONTROL WITH RANDOM JUMPS

A necessary maximum principle is given for nonzero-sum stochastic differential games with random jumps.The result is applied to solve the H_2/H_∞ control problem of stochastic systems with random jumps.A necessary and sufficient condition for the existence of a unique solution to the H_2/H_∞ control problem is derived.The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.     

MAXIMUM PRINCIPLE FOR STOCHASTIC OPTIMAL CONTROL PROBLEM WITH DISTRIBUTED DELAYS

This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.