The dynamic programming equation for stochastic optical control in hilbert spaces: a variational approach
Gianluca Gorni · Stochastics · 1985
The global existence of a point wise solution to the Hamilton-Jacobi equation for totally observed controlled diffusions in Hilbert spaces is proved by studying the corresponding control problem. The optimality principle for the control problem leads to local results, whilst an a priori bound is achieved by introducing a secondary minimization problem.