  Long memory processes driven by L\'evy noise with finite second-order moments
have been well studied in the literature. They form a very rich class of
processes presenting an autocovariance function which decays like a power
function. Here, we study a class of L\'evy process whose second-order moments
are infinite, the so-called $\alpha$-stable processes. Based on Samorodnitsky
and Taqqu (2000), we construct an isometry that allows us to define stochastic
integrals concerning the linear fractional stable motion using
Riemann-Liouville fractional integrals. With this construction, follows
naturally an integration by parts formula. We then present a family of
stationary $S\alpha S$ processes with the property of long-range dependence,
using a generalized measure to investigate its dependence structure. In the
end, the law of large number's result for a time's sample of the process is
shown as an application of the isometry and integration by parts formula.
