We present a very short derivation of the integral representation of the two-sided Skorokhod reflection Z of a continuous function X of bounded variation, which is a generalization of the integral representation of the one-sided map featured in Anantharam and Konstantopoulos (2011) and Konstantopoulos et al. (1996). We also show that Z satisfies a simpler integral representation when additional conditions are imposed on X.
"A note on integral representations of the Skorokhod map." J. Appl. Probab. 53 (1) 293 - 298, March 2016.