  We consider the stochastic integrals of multivariate point processes and
study their concentration phenomena. In particular, we obtain a Bernstein type
of concentration inequality through Dol\'eans-Dade exponential formula and a
uniform exponential inequality using a generic chaining argument. As
applications, we obtain a upper bound for a sequence of discrete time
martingales indexed by a class of functionals, and so derive the rate of
convergence for nonparametric maximum likelihood estimators, which is an
improvement of earlier work of van de Geer.
