Central limit theorems for approximate quadratic variations of pure jump Itô semimartingales
type: Item
instance of: scholarly article
title: Central limit theorems for approximate quadratic variations of pure jump Itô semimartingales
zbMATH Open document ID: 1274.60063
author: Assane Diop
author: Jean Jacod
author: Viktor Todorov
published in: Stochastic Processes and their Applications
publication date: 2013-03-06T00:00:00Z
review text: In this work central limit theorems for the discretization error of the quadratic variation are developed. The authors focus on Itô semimartingales with vanishing continuous martingale part and the discrete-time approximation of quadratic variation from regularly spaced high-frequency observations. Functional central limit theorems are established for two distinct cases. For processes of finite variation involving a drift the discretization error from n observations converges with rate n to a limiting process which comprises a term induced by the drift and a cross term induced by jumps and the drift. For infinite variation processes or a vanishing drift different rates of convergence and limiting processes are deduced.
reviewed by: Mathias Trabs
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 6142012
zbMATH Keywords: Quadratic variation
zbMATH Keywords: Itô semimartingale
zbMATH Keywords: pure jump processes
zbMATH Keywords: approximate quadratic variation
zbMATH Keywords: central limit theorem
zbMATH Keywords: stable convergence in law
MaRDI profile type: Publication
full work available at URL: j.spa.2012.11.003
OpenAlex ID: W2041420518
DOI: 10.1016/J.SPA.2012.11.003
description: scientific article; zbMATH DE number 6142012