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

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 $X_t=\int \int f(A,t-s)\Lambda (dA,ds)$. 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.

References in corpus (1)

• Multivariate supOU processes