Spectral Representation of Multivariate Regularly Varying Lévy and CARMA Processes

Florian Fuchs () and Robert Stelzer ()
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Florian Fuchs: Technische Universität München
Robert Stelzer: Ulm University

Journal of Theoretical Probability, 2013, vol. 26, issue 2, 410-436

Abstract: 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.

Keywords: CARMA process; Lévy process; Spectral representation; Multivariate regular variation; Random noise; Random orthogonal measure; 60G10; 60G51; 62M15; 60G57 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0369-0

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