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.
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This research is partially supported by NSF grant DMS-1007563.
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Pal, S. Concentration for multidimensional diffusions and their boundary local times. Probab. Theory Relat. Fields 154, 225–254 (2012). https://doi.org/10.1007/s00440-011-0368-1
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DOI: https://doi.org/10.1007/s00440-011-0368-1
Keywords
- Concentration of diffusions
- Concentration of local times
- Transportation cost inequality
Mathematics Subject Classification (2000)
- 60G17
- 60G60