OPTIMAL CONTINUOUS-PARAMETER STOCHASTIC CONTROL

Author considers a class of problems which can be treated by methods of partial differential equations, of parabolic or elliptic type. In such problems the process to be optimalli controlled is modelled by some continuous Markow process (generally vectorvalues)/ When the states of the Markov process being controlled are completely observable by the controller, the relevant partial differential equation and boundary data can be formally deduced by dynamic programming. Using rather recent developments in the theories of continuous Markov processes and partial differential equations, the dynamic programming formalisms has been put on rigorous basis provided the partial differential operators appearing satisfy a uniform ellipticity condition.