Weak convergence of sequences of semimartingales with applications to multitype branching processes. (English) Zbl 0595.60008

Joffe, A.; Métivier, M.

Adv. Appl. Probab. 18, 20-65 (1986).

The paper deals with the weak convergence of sequences of cadlag stochastic processes. At first, for the convenience of the readers, some classical results on the ”general theory” of stochastic processes are given. Then a rather detailed exposition of recent results on tightness with particular attention to the case of sequences of semimartingales is presented.
Further the class of the so-called D-semimartingales is introduced and the problem of weak convergence and tightness for sequences of such processes is discussed. Applications to multitype branching processes as well as various examples are given.
For other results on the subject see the paper by B. Grigelionis and R. Mikulavichyus, Litov. Mat. Sb. 21, No.3, 9-24 (1981; Zbl 0498.60005).

Reviewer: R.Morkvėnas

MSC:

60B10	Convergence of probability measures
60G07	General theory of stochastic processes
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

weak convergence of sequences of cadlag stochastic processes; tightness; multitype branching processes

Citations:

Zbl 0498.60005