{"paper":{"title":"Limit theorems for affine Markov walks conditioned to stay positive","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"\\'Emile Le Page, Ion Grama, Ronan Lauvergnat","submitted_at":"2016-01-12T18:33:06Z","abstract_excerpt":"Consider the real Markov walk $S_n = X_1+ \\dots+ X_n$ with increments $\\left(X_n\\right)_{n\\geq 1}$ defined by a stochastic recursion starting at $X_0=x$. For a starting point $y>0$ denote by $\\tau_y$ the exit time of the process $\\left( y+S_n \\right)_{n\\geq 1}$ from the positive part of the real line. We investigate the asymptotic behaviour of the probability of the event $\\tau_y \\geq n$ and of the conditional law of $y+S_n$ given $\\tau_y \\geq n$ as $n \\to +\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02991","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"}