## Osaka Journal of Mathematics

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

#### 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.

#### Article information

Source
Osaka J. Math., Volume 53, Number 4 (2016), 941-970.

Dates
First available in Project Euclid: 4 October 2016

https://projecteuclid.org/euclid.ojm/1475601825

Mathematical Reviews number (MathSciNet)
MR3554850

Zentralblatt MATH identifier
1362.60038

#### Citation

Boedihardjo, H.; Geng, X.; Qian, Z. Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities. Osaka J. Math. 53 (2016), no. 4, 941--970. https://projecteuclid.org/euclid.ojm/1475601825

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