用随机神经网络逼近随机过程，可量化误差并用于疫情预测。
Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
- 设计带随机系数的神经网络算子，激活函数为S形函数。
- 在均方意义下实现逼近，误差与过程连续性模相关。
- 适用于疫情等随机过程建模，适合对不确定性建模的研究者。
本文构建了一类由S形函数激活的随机系数神经网络算子（SINNOs），在二阶随机过程空间 $ L^2(Ω, /mathcal{F},/mathbb{P}) $ 内建立了其有界性、插值精度与逼近能力，涵盖均方意义、概率意义及路径层面。通过过程的连续性模给出了误差的定量估计。结果表明SINNOs在逼近随机过程方面具有有效性，潜在应用于新冠疫情病例预测。
原文摘要 · Abstract (English)
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.
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