Weak convergence of some classes of martingales with jumps

This paper deals with weak convergence of stochastic integrals with respect to multivariate point processes. The results are given in terms of an entr opy condition for partitioning of the index set of the integrands, which is a sort of L-2-bracketing. We also consider l(infinity)-valued martingale d ifference arrays, and present natural generalizations of Jain-Marcus's and Ossiander's central limit theorems. As an application, the asymptotic behav ior of log-likelihood ratio random fields in general statistical experiment s with abstract parameters is derived.