{"paper":{"title":"Rate of escape and central limit theorem for the supercritical Lamperti problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew R. Wade, Mikhail V. Menshikov","submitted_at":"2009-11-13T12:26:15Z","abstract_excerpt":"The study of discrete-time stochastic processes on the half-line with mean drift at $x$ given by $\\mu_1 (x) \\to 0$ as $x \\to \\infty$ is known as Lamperti's problem. We give sharp almost-sure bounds for processes of this type in the case where $\\mu_1 (x)$ is of order $x^{-\\beta}$ for some $\\beta \\in (0,1)$. The bounds are of order $t^{1/(1+\\beta)}$, so the process is super-diffusive but sub-ballistic (has zero speed). We make minimal assumptions on the moments of the increments of the process (finiteness of $(2+2\\beta+\\varepsilon)$-moments for our main results, so 4th moments certainly suffice)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2599","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"}