Abstract
We consider the functional regular variation in the space \(\mathbb {D}\) of càdlàg functions of multivariate mixed moving average (MMA) processes of the type \(X_t = \int \int f(A, t - s) \Lambda (d A, d s)\). We give sufficient conditions for an MMA process \((X_t)\) to have càdlàg sample paths. As our main result, we prove that \((X_t)\) is regularly varying in \(\mathbb {D}\) if the driving Lévy basis is regularly varying and the kernel function f satisfies certain natural (continuity) conditions. Finally, the special case of supOU processes, which are used, e.g., in applications in finance, is considered in detail.
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Moser, M., Stelzer, R. Functional regular variation of Lévy-driven multivariate mixed moving average processes. Extremes 16, 351–382 (2013). https://doi.org/10.1007/s10687-012-0165-y
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DOI: https://doi.org/10.1007/s10687-012-0165-y