## A Stochastic Optimal Control Problem for the Heat Equation on the Halfline with Dirichlet Boundary-noise and Boundary-control

##### Authors
Masiero, Federica
##### Description
We consider a controlled state equation of parabolic type on the halfline $(0,+\infty)$ with boundary conditions of Dirichlet type in which the unknown is equal to the sum of the control and of a white noise in time. We study finite horizon and infinite horizon optimal control problem related by menas of backward stochastic differential equations.
##### Keywords
Mathematics - Probability, Mathematics - Optimization and Control