Weak convergence of sequences of semimartingales with applications to multitype branching processes

Abstract

The paper is devoted to a systematic discussion of recently developed techniques for the study of weak convergence of sequences of stochastic processes. The methods described make essential use of the semimartingale structure of the processes. Sufficient conditions for tightness including the results of Rebolledo are derived. The techniques are applied to a special class of processes, namely the D-semimartingales. Applications to multitype branching processes are given.