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Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes


Author: Yuzuru Inahama
Journal: Trans. Amer. Math. Soc. 367 (2015), 8107-8137
MSC (2010): Primary 60F10, 60H07, 60H99, 60J60
Published electronically: March 24, 2015
MathSciNet review: 3391911
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Abstract: Since T. Lyons invented rough path theory, one of its most successful applications is a new proof of Freidlin-Wentzell's large deviation principle for diffusion processes. In this paper we extend this method to the case of pinned diffusion processes under a mild ellipticity assumption. Besides rough path theory, our main tool is quasi-sure analysis, which is a kind of potential theory in Malliavin calculus.


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Yuzuru Inahama
Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
Email: inahama@math.nagoya-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-2015-06290-4
Keywords: Large deviation principle, pinned diffusion process, stochastic differential equation, rough path theory, quasi-sure analysis
Received by editor(s): April 1, 2013
Received by editor(s) in revised form: September 6, 2013
Published electronically: March 24, 2015
Article copyright: © Copyright 2015 American Mathematical Society