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We construct a quasi-sure version (in the sense of Malliavin) of geometricrough paths associated with a Gaussian process with long-time memory. As anapplication we establish a large deviation principle (LDP) for capacities forsuch Gaussian rough paths. Together with Lyons' universal limit theorem, ourresults yield immediately the corresponding results for pathwise solutions tostochastic differential equations driven by such Gaussian process in the senseof rough paths. Moreover, our LDP result implies the result of Yoshida on theLDP for capacities over the abstract Wiener space associated with such Gaussianprocess.

Quasi-sure Existence of Gaussian Rough Paths and Large Deviation Principles for Capacities