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Asymptotic equivalence for pure jump Lévy processes with unknown Lévy density and Gaussian white noise

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  • Mariucci, Ester

Abstract

The aim of this paper is to establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Lévy process and a Gaussian white noise experiment observed up to a time T, with T tending to ∞. These approximations are given in the sense of the Le Cam distance, under some smoothness conditions on the unknown Lévy density. All the asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.

Suggested Citation

  • Mariucci, Ester, 2016. "Asymptotic equivalence for pure jump Lévy processes with unknown Lévy density and Gaussian white noise," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 503-541.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:2:p:503-541
    DOI: 10.1016/j.spa.2015.09.009
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    References listed on IDEAS

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    1. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    2. Efromovich, Sam & Samarov, Alex, 1996. "Asymptotic equivalence of nonparametric regression and white noise model has its limits," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 143-145, June.
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