{"paper":{"title":"Limit theorems for Markov walks conditioned to stay positive under a spectral gap assumption","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":"2016-07-26T15:32:30Z","abstract_excerpt":"Consider a Markov chain $(X_n)_{n\\geqslant 0}$ with values in the state space $\\mathbb X$. Let $f$ be a real function on $\\mathbb X$ and set $S_0=0,$ $S_n = f(X_1)+\\cdots + f(X_n),$ $n\\geqslant 1$. Let $\\mathbb P_x$ be the probability measure generated by the Markov chain starting at $X_0=x$. For a starting point $y \\in \\mathbb R$ denote by $\\tau_y$ the first moment when the Markov walk $(y+S_n)_{n\\geqslant 1}$ becomes non-positive. Under the condition that $S_n$ has zero drift, we find the asymptotics of the probability $\\mathbb P_x ( \\tau_y >n )$ and of the conditional law $\\mathbb P_x ( y+S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07757","kind":"arxiv","version":2},"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"}