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We consider the functional regular variation in the space $\mathbb{D}$ ofc\`adl\`ag functions of multivariate mixed moving average (MMA) processes ofthe type $X_t = \int\int f(A, t - s) \Lambda (d A, d s)$. We give sufficientconditions for an MMA process $(X_t)$ to have c\`adl\`ag sample paths. As ourmain result, we prove that $(X_t)$ is regularly varying in $\mathbb{D}$ if thedriving L\'evy basis is regularly varying and the kernel function $f$ satisfiescertain natural (continuity) conditions. Finally, the special case of supOUprocesses, which are used, e.g., in applications in finance, is considered indetail.

FunctionaL Regular Variation of L\'evy-driven Multivariate Mixed Moving Average Processes