  In the recent papers [Lochowski:2011fk, Lochowski:2013yq, Lochowski:2013lr]
the truncated variation has been introduced, characterized and studied in
various stochastic settings. In this note we uncover an intimate link to the
Skorokhod problem. Further, we exploit it to give an explicit representation of
the truncated variation of a Brownian motion. More precisely, we prove that the
inverse of this process is, up to a minor time shift, a L\'evy subordinator
with the exponent \sqrt{2q}\tanh(c\sqrt{q/2}) . This also gives a
representation of a solution of the two-sided Skorokhod problem for a Brownian
motion.
