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Riemann-integration and a new proof of the Bichteler–Dellacherie theorem

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  • Beiglböck, M.
  • Siorpaes, P.

Abstract

We give a new proof of the celebrated Bichteler–Dellacherie theorem, which states that a process S is a good integrator if and only if it is the sum of a local martingale and a finite-variation process. As a corollary, we obtain a characterization of semimartingales along the lines of classical Riemann integrability.

Suggested Citation

  • Beiglböck, M. & Siorpaes, P., 2014. "Riemann-integration and a new proof of the Bichteler–Dellacherie theorem," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1226-1235.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:3:p:1226-1235
    DOI: 10.1016/j.spa.2013.10.001
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    References listed on IDEAS

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    1. Beiglböck, Mathias & Schachermayer, Walter & Veliyev, Bezirgen, 2012. "A short proof of the Doob–Meyer theorem," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1204-1209.
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    Cited by:

    1. Christoph Kuhn & Alexander Molitor, 2020. "Semimartingale price systems in models with transaction costs beyond efficient friction," Papers 2001.03190, arXiv.org, revised Aug 2021.
    2. Christoph Kühn & Alexander Molitor, 2022. "Semimartingale price systems in models with transaction costs beyond efficient friction," Finance and Stochastics, Springer, vol. 26(4), pages 927-982, October.

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