Busy periods of fractional Brownian storage: a large deviations approach

The present paper might be the rst one where such an analysis is attempted on the distribution of a busy period of fractional Brownian storage. Our technical framework here is the theory of large deviations in path space of a Gaussian process. The inspiration for doing this came from reading the recent book by A. Shwartz and A. Weiss [SW95]. It deals, however, only with Markovian systems, and the general theory must in our case be taken from the world of general Gaussian processes.