In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well as path-wise within the space of second-order stochastic (random) processes \( L^2(Ω, \mathcal{F},\mathbb{P}) \). Additionally, we provide quantitative error estimates using the modulus of continuity of the processes. These results highlight the effectiveness of SINNOs for approximating stochastic processes with potential applications in COVID-19 case prediction.

翻译：本文构建了一类由S型函数激活、具有随机系数的随机插值神经网络算子（SINNOs）。我们在二阶随机过程空间 \( L^2(Ω, \mathcal{F},\mathbb{P}) \) 中，建立了该类算子在均方意义、概率意义以及路径意义上的有界性、插值精度与逼近能力。此外，我们利用过程的连续模给出了定量的误差估计。这些结果凸显了SINNOs在逼近随机过程方面的有效性，在COVID-19病例预测等领域具有潜在应用价值。