Title: Duality and upper bounds in optimal stochastic control governed by partial differential equations,
Abstract: A dual control problem is presented for the optimal stochastic control of a
system governed by partial differential equations. Relationships between the
optimal values of the original and the dual problems are investigated and two
duality theorems are proved. The dual problem serves to provide upper bounds
for the optimal and maximum value of the original one or even to give the
optimal value.