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Erschienen in:
2012 | OriginalPaper | Buchkapitel
The Central Limit Theorem for Functions of an Increasing Number of Increments
verfasst von : Jean Jacod, Philip Protter
Erschienen in: Discretization of Processes
Verlag: Springer Berlin Heidelberg
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Here we study the same problem as in the previous chapter, except that now the functionals depend on an increasing number
k
n
of increments, with
kj
n
→∞ and
k
n
Δ
n
→0.
In this setting, the Central Limit Theorems are considerably more difficult to prove, and the rate of convergence becomes
$\sqrt{k_{n} \varDelta _{n}}$
instead of
$\sqrt {\varDelta _{n}}$
. 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 a necessary step for studying semimartingales contaminated by an observation noise, and we treat this in Chap.
16
.