  Linear multivariate Hawkes processes (MHP) are a fundamental class of point
processes with self-excitation. When estimating parameters for these processes,
a difficulty is that the two main error functionals, the log-likelihood and the
least squares error (LSE), as well as the evaluation of their gradients, have a
quadratic complexity in the number of observed events. In practice, this
prohibits the use of exact gradient-based algorithms for parameter estimation.
We construct an adaptive stratified sampling estimator of the gradient of the
LSE. This results in a fast parametric estimation method for MHP with general
kernels, applicable to large datasets, which compares favourably with existing
methods.
