The Central Limit Theorem for Functions of an Increasing Number of Increments

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 67)

Abstract

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.

Keywords

Central Limit Theorem Homogeneous Function Polynomial Growth Auxiliary Space Stable Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut de MathématiquesUniversité Paris VI – Pierre et Marie CurieParisFrance
  2. 2.Department of StatisticsColumbia UniversityNew YorkUSA

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