{"paper":{"title":"Self-intersection local times for Volterra Gaussian processes in stochastic flows with interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.PR","authors_text":"Olga Izyumtseva, Wasiur R. KhudaBukhsh","submitted_at":"2026-06-01T10:25:28Z","abstract_excerpt":"In this paper, we study self-intersection local times for a stochastic process $x(u(\\cdot),t)$, where $u$ is a Gaussian process of the form $u(t)=\\int^t_0k(t,s)\\mathrm{d}{w(s)}$, $k$ is a deterministic kernel of the Volterra type, $w$ is a Wiener process, and $x$ is a solution to the \\emph{equation with interaction}. Equations with interaction are a class of interacting particle system described by stochastic differential equations whose coefficients depend on a random measure (initial distribution of particles) transformed by the flow of solutions. Considering the occupation measure of $u$ as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02036","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02036/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}