  In this paper we find and develop a stochastic integral representation for
the class of strictly stable distributions. We establish an explicit
relationship between stochastic integral and shot-noise series representations
of strictly stable distributions, which shows that the class of distributions
representable by stochastic integral is larger than the class representable by
a shot-noise series. This inclusion is proper when the stability index is
greater than 1. We also give an explicit description of distributions
possessing both representations.
