{"paper":{"title":"Transformations of L\\'evy Processes","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Michael Sch\\\"urmann, Michael Skeide, Silvia Volkwardt","submitted_at":"2007-12-20T17:21:27Z","abstract_excerpt":"A L\\'evy process on a *-bialgebra is given by its generator, a conditionally positive hermitian linear functional vanishing at the unit element. A *-algebra homomorphism k from a *-bialgebra C to a *-bialgebra B with the property that k respects the counits maps generators on B to generators on C. A tranformation between the corrresponding two L\\'evy processes is given by forming infinitesimal convolution products.\n  This general result is applied to various situations, e.g., to a *-bialgebra and its associated primitive tensor *-bialgebra (called \"generator process\") as well as its associated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.3504","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"}