  We prove that probability laws of certain multidimensional semimartingales
which includes time-inhomogenous diffusions, under suitable assumptions,
satisfy Quadratic Transportation Cost Inequality under the uniform metric. From
this we derive concentration properties of Lipschitz functions of process paths
that depend on the entire history. In particular, we estimate concentration of
boundary local time of reflected Brownian motions on a polyhedral domain. We
work out explicit applications of consequences of measure concentration for the
case of Brownian motion with rank-based drifts.
