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On the lack of semimartingale property

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  • Prokaj, Vilmos
  • Bondici, László

Abstract

In this work we extend the characterization of semimartingale functions in Çinlar et al. (1980) to the non-Markovian setting. We prove that if a function of a semimartingale remains a semimartingale, then under certain conditions the function must have intervals where it is a difference of two convex functions. Under suitable conditions this property also holds for random functions. As an application, we prove that the median process defined in Prokaj et al. (2011) is not a semimartingale. The same process appears also in Hu and Warren (2000) where the question of the semimartingale property is raised but not settled.

Suggested Citation

  • Prokaj, Vilmos & Bondici, László, 2022. "On the lack of semimartingale property," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 335-359.
    • Handle: RePEc:eee:spapps:v:146:y:2022:i:c:p:335-359
    DOI: 10.1016/j.spa.2022.01.009
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    References listed on IDEAS

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    1. Hu, Yueyun & Warren, Jon, 2000. "Ray-Knight theorems related to a stochastic flow," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 287-305, April.
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    Cited by:

    1. David Criens & Mikhail Urusov, 2022. "Separating Times for One-Dimensional Diffusions," Papers 2211.06042, arXiv.org, revised May 2023.

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