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Lévy driven CARMA generalized processes and stochastic partial differential equations

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  • Berger, David

Abstract

We give a new definition of a Lévy driven CARMA random field, defining it as a generalized solution of a stochastic partial differential equation (SPDE). Furthermore, we give sufficient conditions for the existence of a mild solution of our SPDE. Our model unifies all known definitions of CARMA random fields, and in particular for dimension 1 we obtain the classical CARMA process.

Suggested Citation

  • Berger, David, 2020. "Lévy driven CARMA generalized processes and stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 5865-5887.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:5865-5887
    DOI: 10.1016/j.spa.2020.04.009
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    References listed on IDEAS

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    1. Klepsch, J. & Klüppelberg, C. & Wei, T., 2017. "Prediction of functional ARMA processes with an application to traffic data," Econometrics and Statistics, Elsevier, vol. 1(C), pages 128-149.
    2. Brockwell, Peter J. & Lindner, Alexander, 2009. "Existence and uniqueness of stationary Lévy-driven CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2660-2681, August.
    3. M. Ghahramani & A. Thavaneswaran, 2006. "Financial applications of ARMA models with GARCH errors," Journal of Risk Finance, Emerald Group Publishing, vol. 7(5), pages 525-543, November.
    4. Peter J. Brockwell & Vincenzo Ferrazzano & Claudia Klüppelberg, 2013. "High-frequency sampling and kernel estimation for continuous-time moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 385-404, May.
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    Cited by:

    1. Fageot, Julien & Humeau, Thomas, 2021. "The domain of definition of the Lévy white noise," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 75-102.

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