2025/12/11 by Quanjun Lang, Lang, Quanjun, Jianfeng Lu +1
Physics and Astronomy · Mathematics · Economics, Econometrics and Finance · #Model Reduction and Neural Networks #Markov Chains and Monte Carlo Methods #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2512.10256
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.