Convergence of Processes with Independent Increments

  • Jean Jacod
  • Albert N. Shiryaev
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 288)


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.


Characteristic Function Poisson Process Fixed Time Central Limit Theorem Dense Subset 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Jean Jacod
    • 1
  • Albert N. Shiryaev
    • 2
  1. 1.Laboratoire de ProbabilitésParis 05France
  2. 2.Steklov Mathematical InstituteMoscowUSSR

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