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

Research output: Contribution to journalReview article

1 Citation (Scopus)

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 - Jan 1 2016

Fingerprint

Rough Paths
Large Deviation Principle
Delta Function
Pullback
Large Deviations
Diffusion Process
Path Space
Wiener Space
Borel Measure
Scale Parameter
Small Parameter
Corollary
Tend
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Large Deviations for Rough Path Lifts of Watanabe's Pullbacks of Delta Functions. / Inahama, Yuzuru.

In: International Mathematics Research Notices, Vol. 2016, No. 20, 01.01.2016, p. 6378-6414.

Research output: Contribution to journalReview article

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