Concentration for multidimensional diffusions and their boundary local times

Abstract

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.

25 pages, Revised version

References in corpus (4)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Atlas models of equity markets
• Characterization of invariant measures at the leading edge for competing particle systems
• Concentration of measure for systems of Brownian particles interacting through their ranks