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We establish a sample path generation scheme in a unified manner for generalmultivariate infinitely divisible processes based on shot noise representationof their integrators. The approximation is derived from the decomposition ofthe infinitely divisible process to three independent components based on jumpsizes and timings: the large jumps over a compact time interval, small jumpsover the entire time interval and large jumps over an unbounded time interval.The first component is taken as the approximation and is much simpler thansimulation of general Gaussian processes, while the latter two components areanalyzed as the error. We derive technical conditions for the two error termsto vanish in the limit and for the scaled component on small jumps to convergeto a Gaussian process so as to enhance the accuracy of the weak approximation.We provide an extensive collection of examples to highlight the widepracticality of the proposed approach.

A general approach to sample path generation of infinitely divisible processes via shot noise representation