Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this development, we study a deep neural network method to estimate the drift coefficient of a multi-dimensional diffusion process from discrete observations. We derive generalization error bounds for least squares estimates based on deep neural networks and show that they achieve the minimax rate of convergence up to a logarithmic factor when the drift function has a compositional structure.

翻译：近年来，众多研究揭示了深度神经网络方法在非参数回归模型中的高度自适应性，并验证了其在多种函数类上的优越性能。受此启发，我们研究了一种利用深度神经网络从离散观测中估计多维扩散过程漂移系数的方法。我们推导出基于深度神经网络的最小二乘估计的泛化误差界，并证明当漂移函数具有组合结构时，该估计能够达到（至多相差对数因子）极小极大收敛速度。