{"paper":{"title":"The Kingman tree length process has infinite quadratic variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Wakolbinger, Iulia Dahmer, Robert Knobloch","submitted_at":"2014-02-10T11:28:11Z","abstract_excerpt":"In the case of neutral populations of fixed sizes in equilibrium whose genealogies are described by the Kingman $N$-coalescent back from time $t$ consider the associated processes of total tree length as $t$ increases. We show that the (c\\`adl\\`ag) process to which the sequence of compensated tree length processes converges as $N$ tends to infinity is a process of infinite quadratic variation; therefore this process cannot be a semimartingale. This answers a question posed in Pfaffelhuber et al. (2011)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2113","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"}