{"paper":{"title":"Power and exponential moments of the number of visits and related quantities for perturbed random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Gerold Alsmeyer, Matthias Meiners","submitted_at":"2011-11-17T17:22:59Z","abstract_excerpt":"Let $(\\xi_1,\\eta_1),(\\xi_2,\\eta_2),...$ be a sequence of i.i.d.\\ copies of a random vector $(\\xi,\\eta)$ taking values in $\\R^2$, and let $S_n := \\xi_1+...+\\xi_n$. The sequence $(S_{n-1} + \\eta_n)_{n \\geq 1}$ is then called perturbed random walk.\n  We study random quantities defined in terms of the perturbed random walk: $\\tau(x)$, the first time the perturbed random walk exits the interval $(-\\infty,x]$, $N(x)$, the number of visits to the interval $(-\\infty,x]$, and $\\rho(x)$, the last time the perturbed random walk visits the interval $(-\\infty,x]$. We provide criteria for the a.s.\\ finitene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4159","kind":"arxiv","version":3},"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"}