= Skorokhod reflection map on the half-line
{c}
{title2=$\Gamma(g)(t)=g(t)+\sup_{s\le t}[-g(s)]^+$}
For a <continuous> driving path with $g(0)\ge0$, the running supremum supplies the minimal nondecreasing regulator keeping the path nonnegative. It increases only at a new negative running minimum, where the reflected path is zero. Any regulator satisfying the <Skorokhod problem> constraints must coincide with it. On a finite time interval, $\|\Gamma(g)-\Gamma(h)\|_\infty\le2\|g-h\|_\infty$, so the map is continuous and transfers a <functional central limit theorem> to reflected workloads.
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