Understanding limit theorems for semimartingales: a short survey
Version of Record online: 24 JUN 2010
© 2010 The Authors. Journal compilation © 2010 VVS
Special Issue: Statistical Inference for Lévy Processes with Applications to Finance
Volume 64, Issue 3, pages 329–351, August 2010
How to Cite
Podolskij, M. and Vetter, M. (2010), Understanding limit theorems for semimartingales: a short survey. Statistica Neerlandica, 64: 329–351. doi: 10.1111/j.1467-9574.2010.00460.x
AMS 2000 subject classifications. Primary 60F05, 60G44, 62M09; secondary 60G42, 62G20.
- Issue online: 16 JUL 2010
- Version of Record online: 24 JUN 2010
- Received: October 2009. Revised: February 2010.
- central limit theorem;
- high frequency observations;
- stable convergence
This paper presents a short survey on limit theorems for certain functionals of semimartingales that 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.