Dynamic programming for the stochastic burgers equation

Abstract

We solve a control problem for the stochastic Burgers equation using the dynamic programming approach. The cost functional involves exponentially growing functions and the analog of the kinetic energy; the case of a distributed parameter control is considered. The Hamilton-Jacobi equation is solved by a compactness method and a-priori estimates are obtained thanks to the regularizing properties of the transition semigroup associated to the stochastic Burgers equation; a fixed point argument does not seem to apply here.