Malliavin calculus approach to statistical inference for Levy driven SDE's
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 dXt=aθ(Xt)dt + dZt with a tempered α-stable process Z. Using these representations, regularity of the statistical experiment and the Cramer-Rao inequality are proved.
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