Malliavin calculus approach to statistical inference for Levy driven SDE's

2013/01/22 by D. O. Ivanenko, Ivanenko, D. O., Alexei Kulik +2 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1301.5141

openalex publication_date 2013/01/22 · arxiv created 2013/08/10 · arxiv updated 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 tempered α-stable process Z. Using these representations, regularity of the statistical experiment and the Cramer-Rao inequality are proved.

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• Second derivative of the log-likelihood in the model given by a Levy driven stochastic differential equations

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