{"paper":{"title":"A Feynman--Kac representation of a non-conservative and path-dependent nonlinear reaction-diffusion-advection system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniela Morale, Leonardo Tarquini, Stefania Ugolini","submitted_at":"2024-07-27T17:11:00Z","abstract_excerpt":"We provide a probabilistic interpretation of a weakly parabolic PDE--ODE system with a reaction term, which makes the dynamics non-conservative. As a consequence, the solution is represented as the density of a sub-probability measure solving a Feynman--Kac-type equation, where the time-marginal law of the underlying process is weighted by a survival probability induced by the reaction. This leads to a coupled stochastic formulation consisting of a non-Markovian stochastic differential equation with path-dependent coefficients and the associated Feynman--Kac-type equation. We prove well-posedn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19301","kind":"arxiv","version":3},"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/2407.19301/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"}