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- Title
Large Deviations for Rough Path Lifts of Watanabe's Pullbacks of Delta Functions.
- Authors
Yuzuru Inahama
- Abstract
We study Donsker-Watanabe's delta functions associated with strongly hypoelliptic diffusion processes indexed by a small parameter. They are finite Borel measures on the Wiener space and admit a rough path lift. Our main result is a large deviation principle (LDP) of Schilder type for the lifted measures on the geometric rough path space as the scale parameter tends to zero. As a corollary, we obtain an LDP conjectured by Takanobu and Watanabe, which is a generalization of an LDP of Freidlin-Wentzell type for pinned diffusion processes.
- Subjects
MATHEMATICAL functions; HYPOELLIPTIC differential equations; LARGE deviation theory; BOREL sets; DIFFUSION processes; STOCHASTIC difference equations
- Publication
IMRN: International Mathematics Research Notices, 2016, Vol 2016, Issue 20, p6378
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnv349