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Understanding limit theorems for semimartingales: a short survey
Author(s) -
Podolskij Mark,
Vetter Mathias
Publication year - 2010
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2010.00460.x
Subject(s) - mathematical proof , limit (mathematics) , mathematics , sketch , simple (philosophy) , point (geometry) , convergence (economics) , central limit theorem , state (computer science) , pure mathematics , mathematical economics , calculus (dental) , mathematical analysis , algorithm , epistemology , statistics , medicine , philosophy , geometry , dentistry , economics , economic growth
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.