A general result on the method of randomized stopping is proved. It is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. This is motivated by recent results of Krylov on numerical solutions to the Bellman equation.
"On randomized stopping." Bernoulli 14 (2) 352 - 361, May 2008. https://doi.org/10.3150/07-BEJ108