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Small-time fluctuations for the bridge in a model class of hypoelliptic diffusions of weak Hörmander type
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Habermann, Karen (2019) Small-time fluctuations for the bridge in a model class of hypoelliptic diffusions of weak Hörmander type. Electronic Journal of Probability, 24 (11). pp. 1-19. doi:10.1214/19-EJP274 ISSN 1083-6489.
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Official URL: http://dx.doi.org/10.1214/19-EJP274
Abstract
We study the small-time asymptotics for hypoelliptic diffusion processes conditioned by their initial and final positions, in a model class of diffusions satisfying a weak Hörmander condition where the diffusivity is constant and the drift is linear. We show that, while the diffusion bridge can exhibit a blow-up behaviour in the small time limit, we can still make sense of suitably rescaled fluctuations which converge weakly. We explicitly describe the limit fluctuation process in terms of quantities associated to the unconditioned diffusion. In the discussion of examples, we also find an expression for the bridge from 0 to 0 in time 1 of an iterated Kolmogorov diffusion.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Diffusion processes, Limit theorems (Probability theory), Hypoelliptic operators, Central limit theorem | ||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||
ISSN: | 1083-6489 | ||||||
Official Date: | 2019 | ||||||
Dates: |
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Volume: | 24 | ||||||
Number: | 11 | ||||||
Page Range: | pp. 1-19 | ||||||
DOI: | 10.1214/19-EJP274 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 11 November 2020 | ||||||
Date of first compliant Open Access: | 12 November 2020 | ||||||
RIOXX Funder/Project Grant: |
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