{"paper":{"title":"Regular variation of infinite series of processes with random coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Raluca Balan","submitted_at":"2014-01-30T22:27:37Z","abstract_excerpt":"In this article, we consider a series $X(t)=\\sum_{j \\geq 1}\\Psi_j(t) Z_j(t),t \\in [0,1]$ of random processes with sample paths in the space $D=D[0,1]$ of c\\`adl\\`ag functions (i.e. right-continuous functions with left limits) on $[0,1]$. We assume that $(Z_j)_{j \\geq 1}$ are i.i.d. processes with sample paths in $D$ and $(\\Psi_j)_{j \\geq 1}$ are processes with continuous sample paths. Using the notion of regular variation for $D$-valued random elements (introduced in Hult and Lindskog (2005)), we show that $X$ is regularly varying if $Z_1$ is regularly varying, $(\\Psi_j)_{j \\geq 1}$ satisfy so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8012","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"}