FunctionaL Regular Variation of Lévy-driven Multivariate Mixed Moving Average Processes

2012/04/03 by Robert Stelzer, Stelzer, Robert, Martin Moser +1
Mathematics · #60G51 #60G70 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G51 #msc:60G70

paper · pdf · doi:10.48550/arxiv.1204.0639

arxiv created 2012/04/03 · arxiv updated 2012/04/04

Abstract

We consider the functional regular variation in the space \mathbbD of càdlàg functions of multivariate mixed moving average (MMA) processes of the type X_t = ∫∫ f(A, t - s) Λ(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 \mathbbD 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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