{"paper":{"title":"Martingale-type processes indexed by the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas Basse-O'Connor, Jan Pedersen, Svend-Erik Graversen","submitted_at":"2010-05-02T17:33:09Z","abstract_excerpt":"Some  classes  of increment  martingales,  and the corresponding  localized classes, are studied. An increment martingale is indexed by the real line and its  increment processes are martingales. We focus primarily on the behavior as time goes to minus infinity in relation to  the quadratic variation or the predictable quadratic variation, and we relate the limiting behavior to the martingale property.  Finally, integration with respect to an increment martingale   is studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0150","kind":"arxiv","version":1},"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"}