Central Limit Theorems for approximate quadratic variations of pure jump Itô semimartingales

Assane Diop, Jean Jacod, Viktor Todorov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We derive Central Limit Theorems for the convergence of approximate quadratic variations, computed on the basis of regularly spaced observation times of the underlying process, toward the true quadratic variation. This problem was solved in the case of an Itô semimartingale having a non-vanishing continuous martingale part. Here we focus on the case where the continuous martingale part vanishes and find faster rates of convergence, as well as very different limiting processes.

Original languageEnglish (US)
Pages (from-to)839-886
Number of pages48
JournalStochastic Processes and their Applications
Volume123
Issue number3
DOIs
StatePublished - 2013

Keywords

  • Approximate quadratic variation
  • Central Limit Theorem
  • Itô semimartingale
  • Pure jump processes
  • Quadratic variation
  • Stable convergence in law

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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