{"paper":{"title":"A transience condition for a class of one-dimensional symmetric L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c","submitted_at":"2013-08-21T16:33:15Z","abstract_excerpt":"In this paper, we give a sufficient condition for transience for a class of one-dimensional symmetric L\\'evy processes. More precisely, we prove that a one-dimensional symmetric L\\'evy process with the L\\'evy measure $\\nu(dy)=f(y)dy$ or $\\nu(\\{n\\})=p_n$, where the density function $f(y)$ is such that $f(y)>0$ a.e. and the sequence $\\{p_n\\}_{n\\geq1}$ is such that $p_n>0$ for all $n\\geq1$, is transient if $$\\int_1^{\\infty}\\frac{dy}{y^{3}f(y)}<\\infty\\quad\\textrm{or}\\quad \\sum_{n=1}^{\\infty}\\frac{1}{n^{3}p_n}<\\infty.$$ Similarly, we derive an analogous transience condition for one-dimensional symm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4626","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"}