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Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities
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Boedihardjo, Horatio, Geng, Xi and Qian, Zhongmin (2015) Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities. Osaka Journal of Mathematics, 53 (4). pp. 941-970.
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Official URL: https://projecteuclid.org/euclid.ojm/1475601825
Abstract
We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Statistics | ||||
| Journal or Publication Title: | Osaka Journal of Mathematics | ||||
| Publisher: | Department of Mathematics, Osaka/Osaka City Universities | ||||
| ISSN: | 0030-6126 | ||||
| Official Date: | 15 October 2015 | ||||
| Dates: |
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| Volume: | 53 | ||||
| Number: | 4 | ||||
| Page Range: | pp. 941-970 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Funder: | European Research Council | ||||
| Grant number: | 291244 | ||||
| Open Access Version: |
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