{"ID":2830080,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.10256","arxiv_id":"2512.10256","title":"Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels","abstract":"We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of the memory kernel and are quantitatively bounded by the estimation error of the kernel in a weighted norm. Our analysis integrates synchronized noise coupling with a Volterra comparison theorem, encompassing both subexponential and exponential kernel classes. For first-order models, we derive moment and perturbation bounds using resolvent estimates in weighted spaces. For second-order models with confining potentials, we prove contraction and stability under kernel perturbations using a hypocoercive Lyapunov-type distance. This framework accommodates non-translation-invariant kernels and white-noise forcing, explicitly linking improved kernel estimation to enhanced trajectory prediction. Numerical examples validate these theoretical findings.","short_abstract":"We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of the memory kernel and are quan...","url_abs":"https://arxiv.org/abs/2512.10256","url_pdf":"https://arxiv.org/pdf/2512.10256v1","authors":"[\"Quanjun Lang\",\"Jianfeng Lu\"]","published":"2025-12-11T03:27:58Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.DS\",\"math.NA\",\"math.PR\"]","methods":"[]","has_code":false}