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Convergence to a Semimartingale

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Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 288))

Abstract

Here comes the third—and last—step in our exposition of limit theorems. Not only are the pre-limiting processes X n 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(X) of X So, in most of the chapter, we will assume that ℒ(X) is the unique solution to the martingale problem associated with the characteristics of X, as introduced in Chapter III.

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© 1987 Springer-Verlag Berlin Heidelberg

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Jacod, J., Shiryaev, A.N. (1987). Convergence to a Semimartingale. In: Limit Theorems for Stochastic Processes. Grundlehren der mathematischen Wissenschaften, vol 288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02514-7_9

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  • DOI: https://doi.org/10.1007/978-3-662-02514-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-02516-1

  • Online ISBN: 978-3-662-02514-7

  • eBook Packages: Springer Book Archive

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