{"paper":{"title":"Large excursions and conditioned laws for recursive sequences generated by random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeffrey F. Collamore, Sebastian Mentemeier","submitted_at":"2016-08-18T05:01:26Z","abstract_excerpt":"We determine the large exceedance probabilities and large exceedance paths for the matrix recursive sequence $V_n = M_n V_{n-1} + Q_n, \\: n=1,2,\\ldots,$ where $\\{M_n\\}$ is an i.i.d. sequence of $d \\times d$ random matrices and $\\{ Q_n\\}$ is an i.i.d. sequence of random vectors, both with nonnegative entries. Early work on this problem dates to Kesten's (1973) seminal paper, motivated by an application to multi-type branching processes. Other applications arise in financial time series modeling (connected to the study of the GARCH($p,q$) processes) and in physics, and this recursive sequence ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05175","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"}