  We establish a sample path generation scheme in a unified manner for general
multivariate infinitely divisible processes based on shot noise representation
of their integrators. The approximation is derived from the decomposition of
the infinitely divisible process to three independent components based on jump
sizes and timings: the large jumps over a compact time interval, small jumps
over the entire time interval and large jumps over an unbounded time interval.
The first component is taken as the approximation and is much simpler than
simulation of general Gaussian processes, while the latter two components are
analyzed as the error. We derive technical conditions for the two error terms
to vanish in the limit and for the scaled component on small jumps to converge
to a Gaussian process so as to enhance the accuracy of the weak approximation.
We provide an extensive collection of examples to highlight the wide
practicality of the proposed approach.
