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Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

Boedihardjo, H., Geng, X. and Qian, Z. (2016) Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities. Osaka Journal of Mathematics, 53 (4). ISSN 0030-6126

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Abstract/Summary

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:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:46661
Publisher:Department of Mathematics, Osaka/Osaka City Universities

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