{"paper":{"title":"A Wiener-Hopf Type Factorization for the Exponential Functional of Levy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Juan Carlos Pardo Milan, Mladen Savov, Pierre Patie","submitted_at":"2011-04-30T08:42:45Z","abstract_excerpt":"For a L\\'evy process $\\xi=(\\xi_t)_{t\\geq0}$ drifting to $-\\infty$, we define the so-called exponential functional as follows \\[{\\rm{I}}_{\\xi}=\\int_0^{\\infty}e^{\\xi_t} dt.\\] Under mild conditions on $\\xi$, we show that the following factorization of exponential functionals \\[{\\rm{I}}_{\\xi}\\stackrel{d}={\\rm{I}}_{H^-} \\times {\\rm{I}}_{Y}\\] holds, where, $\\times $ stands for the product of independent random variables, $H^-$ is the descending ladder height process of $\\xi$ and $Y$ is a spectrally positive L\\'evy process with a negative mean constructed from its ascending ladder height process. As "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0062","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"}