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Spectral Representation of Multivariate Regularly Varying Lévy and CARMA Processes

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Abstract

A spectral representation for regularly varying Lévy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail, giving also new insight in the L 2-case where the noise is a random orthogonal measure.

This allows a spectral definition of multivariate regularly varying Lévy-driven continuous time autoregressive moving average (CARMA) processes. It is shown that they extend the well-studied case with finite second moments and coincide with definitions previously used in the infinite variance case when they apply.

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Authors and Affiliations

  1. TUM Institute for Advanced Study & Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Florian Fuchs

  2. Institute of Mathematical Finance, Ulm University, Helmholtzstraße 18, 89081, Ulm, Germany

    Robert Stelzer

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  1. Florian Fuchs
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  2. Robert Stelzer
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Correspondence to Florian Fuchs.

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Fuchs, F., Stelzer, R. Spectral Representation of Multivariate Regularly Varying Lévy and CARMA Processes. J Theor Probab 26, 410–436 (2013). https://doi.org/10.1007/s10959-011-0369-0

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