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.
Original language | English |
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Pages (from-to) | 6378-6414 |
Number of pages | 37 |
Journal | International Mathematics Research Notices |
Volume | 2016 |
Issue number | 20 |
DOIs | |
Publication status | Published - 2016 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)