  We develop a Dickman approximation to the small jumps of multivariate L\'evy
processes and related stochastic integral processes. Further, we show that the
multivariate Dickman distribution is the unique distribution satisfying a
certain stability property and that a related stochastic process is
self-similar. Along the way we develop applications to non-Gaussian
OU-Processes, to the class of generalized multivariate gamma distributions, and
to the popular Barndorff-Nielsen and Shephard stochastic volatility model.
