# Efficient CNN-LSTM based Parameter Estimation of Levy Driven Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2403.04246 · HTML: https://mlsanity.com/paper/2403.04246/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2205.08803/) (2022)
- [Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization](https://mlsanity.com/paper/1408.2441/) (2014)

## Built on by (most cited first, 1 of 1)

- [NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process](https://mlsanity.com/paper/2607.11177/) (2026)

## Abstract (arXiv)

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.