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(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.
Weitere Kapitel dieses Buchs durch Wischen aufrufen
- Convergence to a Semimartingale
Albert N. Shiryaev
- Springer Berlin Heidelberg
- Chapter IX
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