With the fast development of modern deep learning techniques, the study of dynamic systems and neural networks is increasingly benefiting each other in a lot of different ways. Since uncertainties often arise in real world observations, SDEs (stochastic differential equations) come to play an important role. To be more specific, in this paper, we use a collection of SDEs equipped with neural networks to predict long-term trend of noisy time series which has big jump properties and high probability distribution shift. Our contributions are, first, we explored SDEs driven by $\alpha$-stable L\'evy motion to model the time series data and solved the problem through neural network approximation. Second, we theoretically proved the convergence of the model and obtained the convergence rate. Finally, we illustrated our method by applying it to stock marketing time series prediction and found the convergence order of error.
翻译:随着现代深层学习技术的快速发展,动态系统和神经网络的研究正在以许多不同的方式日益相互受益。由于在现实世界观测中经常出现不确定性,SDE(随机差异方程式)将发挥重要作用。更具体地说,在本文件中,我们使用一批装有神经网络的SDE(SDEs)来预测噪音时间序列的长期趋势,这种时间序列具有巨大的跳跃特性和高概率分布变化。首先,我们探索SDEs(SDEs)的驱动力是美元-美元-稳定的L\'evy动作,以模拟时间序列数据,并通过神经网络近似来解决问题。第二,我们理论上证明了模型的趋同,并获得了趋同率。最后,我们用它来储存销售时间序列预测并发现误差的趋同顺序,从而展示了我们的方法。