2003 | OriginalPaper | Buchkapitel
Convergence to a Semimartingale
verfasst von : Jean Jacod, Albert N. Shiryaev
Erschienen in: Limit Theorems for Stochastic Processes
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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Here comes the third—and last—step in our exposition of limit theorems. Not only are the pre-limiting processes Xn arbitrary semimartingales, but the limit process X also is a semimartingale; not quite an arbitrary one, though: since the method is based here on convergence of martingales and on the relations between X and its characteristics, we need these characteristics to indeed characterize the distribution ℒ of X. So, in most of the chapter, we will assume that ℒ is the unique solution to the martingale problem associated with the characteristics of X, as introduced in Chapter III.