{"paper":{"title":"FunctionaL Regular Variation of L\\'evy-driven Multivariate Mixed Moving Average Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Martin Moser, Robert Stelzer","submitted_at":"2012-04-03T09:53:24Z","abstract_excerpt":"We consider the functional regular variation in the space $\\mathbb{D}$ of c\\`adl\\`ag 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 c\\`adl\\`ag sample paths. As our main result, we prove that $(X_t)$ is regularly varying in $\\mathbb{D}$ if the driving L\\'evy 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0639","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}