Concentration for multidimensional diffusions and their boundary local times

Details Concentration for multidimensional diffusions and their boundary local times Concentration for multidimensional diffusions and their boundary local times

2010-05-12

arxiv.org/abs/1005.2217v3

Mathematics

Probability

25 pages, Revised version

Scientific paper

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.

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