{"paper":{"title":"L\\'evy processes conditioned on having a large height process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mathieu Richard","submitted_at":"2011-06-11T15:10:35Z","abstract_excerpt":"In the present work, we consider spectrally positive L\\'evy processes $(X_t,t\\geq0)$ not drifting to $+\\infty$ and we are interested in conditioning these processes to reach arbitrarily large heights (in the sense of the height process associated with $X$) before hitting 0.\n  This way we obtain a new conditioning of L\\'evy processes to stay positive.\n  The (honest) law $\\pfl$ of this conditioned process is defined as a Doob $h$-transform via a martingale. For L\\'evy processes with infinite variation paths, this martingale is $(\\int\\tilde\\rt(\\mathrm{d}z)e^{\\alpha z}+I_t)\\2{t\\leq T_0}$ for some "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2245","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"}