{"paper":{"title":"Occupation time limits of inhomogeneous Poisson systems of independent particles","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Talarczyk, Luis G. Gorostiza, Tomasz Bojdecki","submitted_at":"2006-09-11T14:46:26Z","abstract_excerpt":"We prove functional limits theorems for the occupation time process of a system of particles moving independently in $R^d$ according to a symmetric $\\alpha$-stable L\\'evy process, and starting off from an inhomogeneous Poisson point measure with intensity measure $\\mu(dx)=(1+|x|^{\\gamma})^{-1}dx,\\gamma>0$, and other related measures. In contrast to the homogeneous case $(\\gamma=0)$, the system is not in equilibrium and ultimately it vanishes, and there are more different types of occupation time limit processes depending on arrangements of the parameters $\\gamma, d$ and $\\alpha$. The case $\\ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609290","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"}