{"paper":{"title":"The growth of additive processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ming Yang","submitted_at":"2007-07-26T09:41:54Z","abstract_excerpt":"Let $X_t$ be any additive process in $\\mathbb{R}^d.$ There are finite indices $\\delta_i, \\beta_i, i=1,2$ and a function $u$, all of which are defined in terms of the characteristics of $X_t$, such that\n  \\liminf_{t\\to0}u(t)^{-1/\\eta}X_t^*= \\cases{0, \\quad if $\\eta>\\delta_1$, \\cr\\infty, \\quad if $\\eta<\\delta_2$,}\n  \\limsup_{t\\to0}u(t)^{-1/\\eta}X_t^*= \\cases{0, \\quad if $\\eta>\\beta_2$, \\cr\\infty, \\quad if $\\eta<\\beta_1$,}\\qquad {a.s.},\n  where $X_t^*=\\sup_{0\\le s\\le t}|X_s|.$ When $X_t$ is a L\\'{e}vy process with $X_0=0$, $\\delta_1=\\delta_2$, $\\beta_1=\\beta_2$ and $u(t)=t.$ This is a special cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3886","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"}