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

D. O. Ivanenko () and A. M. Kulik ()
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D. O. Ivanenko: Kyiv National Taras Shevchenko University
A. M. Kulik: Ukrainian National Academy of Sciences

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 1, 107-123

Abstract: 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.

Keywords: Malliavin calculus; Likelihood function; Lévy driven SDE; Regular statistical experiment; Cramer-Rao inequality; 60J75; 60H07; 62F12 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9387-y

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