This study addresses the challenges in parameter estimation of stochastic differential equations driven by non-Gaussian noises, which are critical in understanding dynamic phenomena such as price fluctuations and the spread of infectious diseases. Previous research highlighted the potential of LSTM networks in estimating parameters of alpha stable Levy driven SDEs but faced limitations including high time complexity and constraints of the LSTM chaining property. To mitigate these issues, we introduce the PEnet, a novel CNN-LSTM-based three-stage model that offers an end to end approach with superior accuracy and adaptability to varying data structures, enhanced inference speed for long sequence observations through initial data feature condensation by CNN, and high generalization capability, allowing its application to various complex SDE scenarios. Experiments on synthetic datasets confirm PEnet significant advantage in estimating SDE parameters associated with noise characteristics, establishing it as a competitive method for SDE parameter estimation in the presence of Levy noise.

翻译：本研究针对非高斯噪声驱动的随机微分方程参数估计中的挑战，此类方程在理解价格波动和传染病传播等动态现象中至关重要。先前研究强调了LSTM网络在估计α稳定Levy驱动SDE参数方面的潜力，但存在高时间复杂性和LSTM链式约束等局限性。为缓解这些问题，我们提出了PEnet——一种新颖的基于CNN-LSTM的三阶段模型，该方法通过端到端架构实现了卓越的准确性，并具备对多样数据结构的自适应能力；通过CNN对初始数据进行特征凝聚，提升了长序列观测的推理速度；同时具备高泛化能力，可适用于各种复杂SDE场景。合成数据集上的实验证实了PEnet在估计与噪声特性相关的SDE参数方面的显著优势，使其成为存在Levy噪声条件下SDE参数估计的一种有竞争力的方法。