Error analysis for learning fractional stochastic differential equations with applications in neural approximations
For researchers working on stochastic differential equations and neural approximations, this work provides a rigorous error analysis framework, though it is incremental as it extends existing techniques to fractional SDEs.
This paper develops a unified error analysis framework for learning fractional stochastic differential equations from discrete data, deriving convergence rates that account for time discretization, coefficient approximation, and model fitting errors. Numerical experiments with neural network-based estimation validate the theoretical results.
This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization, coefficient approximation, and model fitting error -- within a unified framework. Through Sobolev-type norms, we derive convergence rates that incorporate the regularity of trajectories, thereby capturing the interaction of these error components. To demonstrate the applicability of the theory, we introduce a training scheme for coefficient function estimation based on shallow neural networks and a recurrent architecture. Numerical experiments validate the theoretical findings and illustrate the effectiveness of the approach.