{"paper":{"title":"A radial invariance principle for non-homogeneous random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aleksandar Mijatovi\\'c, Andrew R. Wade, Nicholas Georgiou","submitted_at":"2017-08-25T10:42:37Z","abstract_excerpt":"Consider non-homogeneous zero-drift random walks in $\\mathbb{R}^d$, $d \\geq 2$, with the asymptotic increment covariance matrix $\\sigma^2 (\\mathbf{u})$ satisfying $\\mathbf{u}^\\top \\sigma^2 (\\mathbf{u}) \\mathbf{u} = U$ and $\\mathrm{tr}\\ \\sigma^2 (\\mathbf{u}) = V$ in all in directions $\\mathbf{u}\\in\\mathbb{S}^{d-1}$ for some positive constants $U<V$. In this paper we establish weak convergence of the radial component of the walk to a Bessel process with dimension $V/U$. This can be viewed as an extension of an invariance principle of Lamperti."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07683","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"}