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High-frequency asymptotics for path-dependent functionals of Ito semimartingales

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  • Moritz Duembgen, University of Cambridge, Storbritannien
  • Mark Podolskij
The estimation of local characteristics of Ito semimartingales has received a great deal of attention in both academia and industry over the past decades. In various papers limit theorems were derived for functionals of increments and ranges in the infill asymptotics setting. In this paper we establish the asymptotic theory for a wide class of statistics that are built from the incremental process of an Ito semimartingale. More specifically, we will show the law of large numbers and the associated stable central limit theorem for the path dependent functionals in the continuous and discontinuous framework. Some examples from economics and physics demonstrate the potential applicability of our theoretical results in practice.
OriginalsprogEngelsk
TidsskriftStochastic Processes and Their Applications
Vol/bind125
Nummer4
Sider (fra-til)1195-1217
Antal sider23
ISSN0304-4149
DOI
StatusUdgivet - 2015

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