Efficient CNN-LSTM based Parameter Estimation of Levy Driven Stochastic
  Differential Equations
Shuaiyu Li Yang Ruan Changzhou Long Yuzhong Cheng
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.