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Universal approximation property of neural stochastic differential equations

Probability 2025-03-24 v1 Machine Learning Functional Analysis Mathematical Finance Machine Learning

Abstract

We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential equations can approximate general stochastic differential equations, both of It\^o diffusion type, arbitrarily well. Moreover, quantitative error estimates are derived for stochastic differential equations with sufficiently regular coefficients.

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Cite

@article{arxiv.2503.16696,
  title  = {Universal approximation property of neural stochastic differential equations},
  author = {Anna P. Kwossek and David J. Prömel and Josef Teichmann},
  journal= {arXiv preprint arXiv:2503.16696},
  year   = {2025}
}

Comments

20 pages

R2 v1 2026-06-28T22:29:02.896Z