Asymptotic inference for multiplicative counting processes based on one realization

It is assumed that we observe one realization of an r dimensional counting process with intensities that are products of predictable and observable weight processes, a common function of time, and predictable functions that depend on an unknown parameter [theta]. Given that the realization brings increasing information on [theta] as the observed time grows asymptotic results are proved for the distributions of parameter estimates, certain test statistics for parametric hypothesis, and goodness-of-fit tests.