{"paper":{"title":"On moments of integral exponential functionals of additive processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Lioudmila Vostrikova (LAREMA), Paavo Salminen","submitted_at":"2018-03-13T14:57:08Z","abstract_excerpt":"For real-valued additive  process  $(X\\_t)\\_{t\\geq 0}$ a recursive equation is derived for the entire positive moments of functionals $$I\\_{s,t}= \\int \\_s^t\\exp(-X\\_u)du, \\quad 0\\leq s<t\\leq\\infty, $$ in case  the Laplace exponent of $X\\_t$ exists for positive values of the parameter. From the equation emergesan easy-to-apply sufficient condition for the finiteness of the  moments. As an application we study  first hitprocesses of  diffusions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04859","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"}