{"paper":{"title":"Occupation times of branching systems with initial inhomogeneous Poisson states and related superprocesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Talarczyk, Luis G. Gorostiza, Tomasz Bojdecki","submitted_at":"2008-09-03T16:31:57Z","abstract_excerpt":"The $(d,\\alpha,\\beta,\\gamma)$-branching particle system consists of particles moving in $R^d$ according to a symmetric $\\alpha$-stable L\\'evy process $(0<\\alpha\\leq 2)$, splitting with a critical $(1+\\beta)$-branching law $(0<\\beta\\leq 1)$, and starting from an inhomogeneous Poisson random measure with intensity measure $\\mu_\\gamma(dx)=dx/(1+|x|^\\gamma), \\gamma\\geq 0$. By means of time rescaling $T$ and Poisson intensity measure $H_T\\mu_\\gamma$, occupation time fluctuation limits for the system as $T\\to\\infty$ have been obtained in two special cases: Lebesgue measure ($\\gamma=0$, the homogeneo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0665","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"}