Titlebook: Discretization of Processes; Jean Jacod,Philip Protter Book 2012 Springer-Verlag Berlin Heidelberg 2012 60F05, 60G44, 60H10, 60H35, 60J75,

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The Central Limit Theorem for Functions of a Finite Number of Incrementsunction is fixed..For unnormalized functionals, studied in Sect. 11.1, this is a rather straightforward extension of the Central Limit Theorems given in Chap. ...In Sect. 11.2, normalized functionals are considered. In this case, the situation is much more complicated than in Chap. ., because two su

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The Central Limit Theorem for Functions of an Increasing Number of Incrementsand ....→0..In this setting, the Central Limit Theorems are considerably more difficult to prove, and the rate of convergence becomes . instead of .. Unnormalized and normalized functionals are studied in Sects. 12.1 and 12.2, respectively..No specific application is given in this chapter, but it is

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Integrated Discretization Errorproper normalization is 1/.., exactly as if . were a non-random function with bounded derivative. In the second case, one would expect the normalizing factor to be ., at least when .≥2: this is what happens when . is continuous, but otherwise the normalizing factor is 1/.., regardless of .≥2.

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Reference work 2020Latest editionUnnormalized and normalized functionals are studied in Sects. 12.1 and 12.2, respectively..No specific application is given in this chapter, but it is a necessary step for studying semimartingales contaminated by an observation noise, and we treat this in Chap. ..

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Renuka Kuber Wazalwar,Priti Pandeyents, is given in Sect. 9.2..Sections 9.3, 9.4 and 9.5 are concerned with a “local approximation” of the volatility, using downward truncated normalized functionals: assuming a suitable regularity of the volatility process .., the aim is to estimate .. (or rather its “square” .). Statistical applications are given in Sect. 9.6.