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Deviation inequalities and the law of iterated logarithm on the path space over a loop group.
- Source :
-
Stochastics: An International Journal of Probability & Stochastic Processes . Dec2005, Vol. 77 Issue 6, p515-536. 22p. - Publication Year :
- 2005
-
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]
Details
- Language :
- English
- ISSN :
- 17442508
- Volume :
- 77
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Stochastics: An International Journal of Probability & Stochastic Processes
- Publication Type :
- Academic Journal
- Accession number :
- 19328601
- Full Text :
- https://doi.org/10.1080/17442500500412399