Florian Fuchs, Robert Stelzer
Published 2011-05-13Version 1
A spectral representation for regularly varying L\'evy 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 L\'evy-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.
On non-negative solutions of SDDEs with an application to CARMA processes
Spectral representation of quasi-infinitely divisible processes
On a spectral representation for correlation measures in configuration space analysis
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