{"paper":{"title":"When a Stochastic Exponential is a True Martingale. Extension of a Method of Bene^s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. Klebaner, R. Liptser","submitted_at":"2011-12-02T11:45:19Z","abstract_excerpt":"Let $\\mathfrak{z}$ be a stochastic exponential, i.e., $\\mathfrak{z}_t=1+\\int_0^t\\mathfrak{z}_{s-}dM_s$, of a local martingale $M$ with jumps $\\triangle M_t>-1$. Then $\\mathfrak{z}$ is a nonnegative local martingale with $\\E\\mathfrak{z}_t\\le 1$. If $\\E\\mathfrak{z}_T= 1$, then $\\mathfrak{z}$ is a martingale on the time interval $[0,T]$. Martingale property plays an important role in many applications. It is therefore of interest to give natural and easy verifiable conditions for the martingale property. In this paper, the property $\\E\\mathfrak{z}_{_T}=1$ is verified with the so-called linear gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0430","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"}