Error analysis for learning fractional stochastic differential equations with applications in neural approximations
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910192683188224 |
|---|---|
| author | Dehshiri, Mahdi Martinez, Kerlyns Viitasaari, Lauri |
| author_facet | Dehshiri, Mahdi Martinez, Kerlyns Viitasaari, Lauri |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error analysis for learning fractional stochastic differential equations with applications in neural approximations Dehshiri, Mahdi Martinez, Kerlyns Viitasaari, Lauri Probability Numerical Analysis 60H10, 65C30, 68T07, 68T05, 65L20, 62G05 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. |
| title | Error analysis for learning fractional stochastic differential equations with applications in neural approximations |
| topic | Probability Numerical Analysis 60H10, 65C30, 68T07, 68T05, 65L20, 62G05 |
| url | https://arxiv.org/abs/2605.04168 |