  We use the abstract method of (local) martingale problems in order to give
criteria for convergence of stochastic processes. Extending previous notions,
the formulation we use is neither restricted to Markov processes (or
semimartingales), nor to continuous or cadlag paths. We illustrate our findings
both, by finding generalizations of known results, and proving new results. For
the latter, we work on processes with fixed times of discontinuity.
