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Malliavin Calculus Approach to Statistical Inference for Lévy Driven SDE’s

Author

Listed:
  • D. O. Ivanenko

    (Kyiv National Taras Shevchenko University)

  • A. M. Kulik

    (Ukrainian National Academy of Sciences)

Abstract

By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discrete time observations of the solution to equation dX t = a θ (X t )dt + dZ t with a Lévy process Z. Using these representations, regularity of the statistical experiment and the Cramer-Rao inequality are proved.

Suggested Citation

  • D. O. Ivanenko & A. M. Kulik, 2015. "Malliavin Calculus Approach to Statistical Inference for Lévy Driven SDE’s," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 107-123, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9387-y
    DOI: 10.1007/s11009-013-9387-y
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    References listed on IDEAS

    as
    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    2. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    3. Simon, Thomas, 2000. "Support theorem for jump processes," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 1-30, September.
    4. repec:dau:papers:123456789/1392 is not listed on IDEAS
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