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.

翻译：我们识别了若干类能够在固定全局线性增长约束下局部一致逼近连续函数的神经网络。对于此类神经网络，其关联的神经随机微分方程能够任意精确地逼近一般随机微分方程，包括伊藤扩散类型。此外，本文推导了具有充分正则系数的随机微分方程的定量误差估计。