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

@inproceedings{Boedihardjo2016QuasisureEO,
  title={Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities},
  author={Horatio S. Boedihardjo and Xiu-hua Geng and Zhihao Qian},
  year={2016}
}
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… CONTINUE READING

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