{"ID":2832247,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.14705","arxiv_id":"2512.14705","title":"The Graph-Embedded Hazard Model (GEHM): Stochastic Network Survival Dynamics on Economic Graphs","abstract":"This paper develops a nonlinear evolution framework for modelling survival dynamics on weighted economic networks by coupling a graph-based $p$-Laplacian diffusion operator with a stochastic structural drift. The resulting finite-dimensional PDE--SDE system captures how node-level survival reacts to nonlinear diffusion pressures while an aggregate complexity factor evolves according to an Itô{} process. Using accretive operator theory, nonlinear semigroup methods, and stochastic analysis, we establish existence and uniqueness of mild solutions, derive topology-dependent energy dissipation inequalities, and characterise the stability threshold separating dissipative, critical, amplifying, and explosive regimes. Numerical experiments on Barabási--Albert networks confirm that hub dominance magnifies nonlinear gradients and compresses stability margins, producing heavy-tailed survival distributions and occasional explosive behaviour.","short_abstract":"This paper develops a nonlinear evolution framework for modelling survival dynamics on weighted economic networks by coupling a graph-based $p$-Laplacian diffusion operator with a stochastic structural drift. The resulting finite-dimensional PDE--SDE system captures how node-level survival reacts to nonlinear diffusion...","url_abs":"https://arxiv.org/abs/2512.14705","url_pdf":"https://arxiv.org/pdf/2512.14705v1","authors":"[\"Diego Vallarino\"]","published":"2025-12-06T12:22:25Z","proceeding":"cs.SI","tasks":"[\"cs.SI\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}