On optimal control of a non-stopped diffusion process with reflection

In the paper the results of [1] are generalized to the multi-dimensional case, when boundary conditions are reduced to reflection in a non-tangential direction $\gamma$. It is supposed that the drift coefficients only are controllable. The method proposed to prove Theorem 1 gives a more effective procedure of finding the optimal value of the performance $\widehat\theta$ than that in [1].