  Using lattice approximations of Euclidean space, we develop a way to
approximate stable processes that are represented by stochastic integrals over
Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show
that the approximations weakly converge as the mesh-size goes to zero. As an
application, we improve upon previous approximation schemes for integrals with
respect to linear fractional stable motions.
