Semimartingale: Itô or not ?

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Itô semimartingales are the semimartingales whose characteristics are absolutely continuous with respect to Lebesgue measure. We study the importance of this assumption for statistical inference on a discretely sampled semimartingale in terms of the identifiability of its characteristics, their estimation, and propose tests of the Itô property against the non-Itô alternative when the observed semimartingale is continuous, or discontinuous with finite activity jumps, and under a number of technical assumptions.

Original languageEnglish (US)
Pages (from-to)233-254
Number of pages22
JournalStochastic Processes and their Applications
Issue number1
StatePublished - Jan 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


  • Absolute continuity
  • Cantor set
  • Discrete sampling
  • High frequency
  • Itô
  • Semimartingale


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