Large Deviations for Rough Path Lifts of Watanabe's Pullbacks of Delta Functions

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    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 languageEnglish
    Pages (from-to)6378-6414
    Number of pages37
    JournalInternational Mathematics Research Notices
    Volume2016
    Issue number20
    DOIs
    Publication statusPublished - 2016

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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