Understanding limit theorems for semimartingales

• Verfasst von: Podolskij, Mark [VerfasserIn]
• Verfasst von: Vetter, Mathias [VerfasserIn]
• Titel: Understanding limit theorems for semimartingales
• Titelzusatz: a short survey
• Verf.angabe: Mark Podolskij, Mathias Vetter
• Umfang: 23 S.
• Fussnoten: Gesehen am 29.05.2018
• Titel Quelle: Enthalten in: Statistica Neerlandica
• Jahr Quelle: 2010
• Band/Heft Quelle: 64(2010), 3, S. 329-351
• ISSN Quelle: 1467-9574
• DOI: doi:10.1111/j.1467-9574.2010.00460.x
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1575814080

Abstract

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.