{"paper":{"title":"Moments for multi-dimensional Mandelbrot's cascades","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chunmao Huang","submitted_at":"2014-05-12T09:15:15Z","abstract_excerpt":"We consider the distributional equation $\\textbf{Z}\\stackrel{d}{=}\\sum_{k=1}^N\\textbf{A}_k\\textbf{Z}(k) $, where $N$ is a random variable taking value in $\\mathbb N_0=\\{0,1,\\cdots\\}$, $\\textbf{A}_1,\\textbf{A}_2,\\cdots$ are $p\\times p$ non-negative random matrix, and $\\textbf{Z},\\textbf{Z}(1),\\textbf{Z}(2),\\cdots$ are $i.i.d$ random vectors in in $\\mathbb{R}_+^p$ with $\\mathbb{R}_+=[0,\\infty)$, which are independent of $(N,\\textbf{A}_1,\\textbf{A}_2,\\cdots)$. Let $\\{\\mathbf Y_n\\}$ be the multi-dimensional Mandelbrot's martingale defined as sums of products of random matrixes indexed by nodes of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2681","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"}