Large Deviation Principle for Fractional Brownian Motion with Respect to Capacity

Abstract

We show that the fractional Brownian motion (fBM) defined via the Volterra integral representation with Hurst parameter Hgeq frac {1}{2} is a quasi-surely defined Wiener functional on the classical Wiener space, and we establish the large deviation principle (LDP) for such an fBM with respect to (p,r)-capacity on the classical Wiener space in Malliavin’s sense.