  We construct a general procedure for the Quasi Likelihood Analysis applied to
a multivariate point process on the real half line in an ergodic framework.
More precisely, we assume that the stochastic intensity of the underlying model
belongs to a family of processes indexed by a finite dimensional parameter.
When a particular family of laws of large numbers applies to those processes,
we establish the consistency, the asymptotic normality and the convergence of
moments of both the Quasi Maximum Likelihood estimator and the Quasi Bayesian
estimator. In addition, we illustrate our main results by showing how they can
be applied to various Limit Order Book models existing in the literature. In
particular, we address the fundamental cases of Markovian models and
exponential Hawkes process-based models.
