{"paper":{"title":"A dynamic model for the two-parameter Dirichlet process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shui Feng, Wei Sun","submitted_at":"2017-06-19T19:18:46Z","abstract_excerpt":"Let $\\alpha=1/2$, $\\theta>-1/2$, and $\\nu_0$ be a probability measure on a type space $S$. In this paper, we investigate the stochastic dynamic model for the two-parameter Dirichlet process $\\Pi_{\\alpha,\\theta,\\nu_0}$. If $S=\\mathbb{N}$, we show that the bilinear form \\begin{eqnarray*} \\left\\{ \\begin{array}{l} {\\cal E}(F,G)=\\frac{1}{2}\\int_{{\\cal P}_1(\\mathbb{N})}\\langle \\nabla F(\\mu),\\nabla G(\\mu)\\rangle_{\\mu} \\Pi_{\\alpha,\\theta,\\nu_0}(d\\mu),\\ \\ F,G\\in {\\cal F},\\\\ {\\cal F}=\\{F(\\mu)=f(\\mu(1),\\dots,\\mu(d)):f\\in C^{\\infty}(\\mathbb{R}^d), d\\ge 1\\} \\end{array} \\right. \\end{eqnarray*} is closable o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06146","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"}