{"paper":{"title":"A Donsker-type Theorem for Log-likelihood Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hanchao Wang, Zhonggen Su","submitted_at":"2017-03-23T08:37:14Z","abstract_excerpt":"Let $(\\Omega, \\mathcal{F}, (\\mathcal{F})_{t\\ge 0}, P)$ be a complete stochastic basis, $X$ a semimartingale with predictable compensator $(B, C, \\nu)$. Consider a family of probability measures $\\mathbf{P}=( {P}^{n, \\psi}, \\psi\\in \\Psi, n\\ge 1)$, where $\\Psi$ is an index set, $ {P}^{n, \\psi}\\stackrel {loc} \\ll{P}$, and denote the likelihood ratio process by $Z_t^{n, \\psi} =\\frac{dP^{n, \\psi}|_{\\mathcal{F}_t}}{d P|_{\\mathcal{F}_t}}$. Under some regularity conditions in terms of logarithm entropy and Hellinger processes, we prove that $\\log Z_t^{n}$ converges weakly to a Gaussian process in $\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07963","kind":"arxiv","version":4},"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"}