{"paper":{"title":"Some aspects of fluctuations of random walks on R and applications to random walks on R+ with non-elastic reflection at 0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kilian Raschel, Marc Peign\\'e, Rim Essifi","submitted_at":"2013-01-24T07:01:21Z","abstract_excerpt":"In this article we refine well-known results concerning the fluctuations of one-dimensional random walks. More precisely, if $(S_n)_{n \\geq 0}$ is a random walk starting from 0 and $r\\geq 0$, we obtain the precise asymptotic behavior as $n\\to\\infty$ of $\\mathbb P[\\tau^{>r}=n, S_n\\in K]$ and $\\mathbb P[\\tau^{>r}>n, S_n\\in K]$, where $\\tau^{>r}$ is the first time that the random walk reaches the set $]r,\\infty[$, and $K$ is a compact set. Our assumptions on the jumps of the random walks are optimal. Our results give an answer to a question of Lalley stated in [9], and are applied to obtain the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5713","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"}