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1. Deviation inequalities and the law of iterated logarithm on the path space over a loop group.

Author

Privault, Nicolas and Xicheng Zhang

Subjects
*LOGARITHMS, *ITERATIVE methods (Mathematics), *WIENER processes, *BROWNIAN motion, *FLUCTUATIONS (Physics)
Abstract

A law of iterated logarithm (LIL) in small time and an asymptotic estimate of modulus of continuity are proved for Brownian motion on the loop group ℒ( G ) over a compact connected Lie group G . Upper bounds are obtained via infinite-dimensional deviation inequalities for functionals on the path space ℙ(ℒ( G )) on ℒ( G ), such as the supremum of Brownian motion on ℒ( G ), which are proved from the Clark–Ocone formula on ℙ(ℒ( G )). The lower bounds rely on analog finite-dimensional results that are proved separately on Riemannian path space. [ABSTRACT FROM AUTHOR]

Published
2005
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