Convergence of Processes with Independent Increments
With this chapter, at least, we enter the subject which has given its name to the whole book. Our final aim is to prove convergence theorems for a sequence of semimartingales toward a semimartingale. We present the material through three successive steps, corresponding to Chapters VII, VIII and IX: firstly, the prelimiting processes, as well of course as the limiting process, have independent increments; secondly, only the limiting process has independent increments; thirdly, the limiting process itself belongs to some rather broad class of semi-martingales.
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