Wat is Singular control, reflected Brownian motion?

A singular control acts through a process of finite variation that increases only on a set of times of Lebesgue measure zero. Reflected Brownian motion on $[-b, b]$ is $X = \sigma W + L - U$, with $L$ and $U$ nondecreasing, increasing only when $X = -b$ and $X = b$ respectively: the minimal pushing that keeps $X$ in the interval.