  As an extension of self-exciting Hawkes process, the multivariate Hawkes
process models counting processes of different types of random events with
mutual excitement. In this paper, we present a perfect sampling algorithm that
can generate i.i.d. stationary sample paths of multivariate Hawkes process
without any transient bias. In addition, we provide an explicit expression of
algorithm complexity in model and algorithm parameters and provide numerical
schemes to find the optimal parameter set that minimizes the complexity of the
perfect sampling algorithm.
