A singular stochastic control problem with state constraints in twodimensions is studied. We show that the value function is C1 and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the optimal stopping problem, we then introduce the associated no-action region and the free boundary and show that, under appropriate conditions, an optimally contr...

A singular stochastic control problem with state constraints in twodimensions is studied. We show that the value function is C1 and its direc­ tional derivatives are the value functions of certain optimal stopping prob­ lems. Guided by the optimal stopping problem, we then introduce the associ­ ated no-action region and the free boundary and show that, under appropriate conditions, an optimally...

A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is C and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the optimal stopping problem, we then introduce the associated no-action region and the free boundary and show that, under appropriate conditions, an optimally contr...

In this paper we study an optimal control problem for a singular diffusion equation associated with total variation energy. The singular diffusion equation is derived as an Allen-Cahn type equation, and then the observing optimal control problem corresponds to a temperature control problem in the solid-liquid phase transition. We show the existence of an optimal control for our singular diffusi...

We study singular perturbations of a class two-scale stochastic control systems with unbounded data. The assumptions are designed to cover some relaxation problems for deep neural networks. construct effective Hamiltonian and initial data prove the convergence value function solution limit (effective) Cauchy problem parabolic equation HJB type. use methods probability, viscosity solutions homog...