Understanding Limit Theorems for Semimartingales: A Short Survey

CREATES Research Paper No. 2009-47

23 Pages Posted: 7 Oct 2009

See all articles by Mark Podolskij

Mark Podolskij

Aarhus University - School of Business and Social Sciences

Mathias Vetter

Ruhr University of Bochum

Date Written: October 6, 2009

Abstract

This paper presents a short survey on limit theorems for certain functionals of semimartingales, which are observed at high frequency. Our aim is to explain the main ideas of the theory to a broader audience. We introduce the concept of stable convergence, which is crucial for our purpose. We show some laws of large numbers (for the continuous and the discontinuous case) that are the most interesting from a practical point of view, and demonstrate the associated stable central limit theorems. Moreover, we state a simple sketch of the proofs and give some examples.

Keywords: central limit theorem, high frequency observations, semimartingale, stable convergence

JEL Classification: C10, C13, C14

Suggested Citation

Podolskij, Mark and Vetter, Mathias, Understanding Limit Theorems for Semimartingales: A Short Survey (October 6, 2009). CREATES Research Paper No. 2009-47, Available at SSRN: https://ssrn.com/abstract=1483590 or http://dx.doi.org/10.2139/ssrn.1483590

Mark Podolskij (Contact Author)

Aarhus University - School of Business and Social Sciences ( email )

Building 350
DK-8000 Aarhus C
Denmark

Mathias Vetter

Ruhr University of Bochum ( email )

Universitätsstraße 150
Bochum, NRW 44780
Germany

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