ABSTRACT
This chapter utilizes "metric entropy" to obtain sufficient conditions and additional necessary conditions for sample boundedness and continuity. It provides sufficient conditions for sample path boundedness and continuity. Metric entropy offers an alternative to integral representation techniques. It has been extensively used in the context of Gaussian processes. Because a-stable processes are closely related to Gaussian processes through conditioning, it is natural to check whether the techniques used in the Gaussian case apply. They do, but the "gap" between the necessary and the sufficient conditions for sample regularity is much greater in the a-stable case than in the Gaussian case.
