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<p>This study tackles key challenges in parameter estimation for stochastic differential equations (SDEs) driven by non-Gaussian noise, which are crucial for modeling dynamic phenomena like price fluctuations and epidemic spread. Traditional quasi-likelihood methods struggle in complex SDE scenarios due to strong assumptions and step-size constraints. Recent data-driven approaches using neural networks have shown promise but face issues like performance degradation on long sequences and limited generalization at domain boundaries. We propose the Multi-level Parameter Estimation Network (MLPEnet), a three-stage model incorporating a parameter heterogeneity condensation phase to improve inference speed and generalization. Experimental results on synthetic datasets indicate that MLPEnet provides better overall accuracy compared to previous methods and effectively reduces performance decline at the boundaries of the training domain, highlighting its potential for broad applicability.</p>

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Multi-level PEnet: A Robust Three-Stage Model for Parameter Estimation in Non-Gaussian Noise-Driven Stochastic Differential Equations

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • Shuaiyu Li,
  • Yuzhong Cheng,
  • Yang Ruan,
  • Hiroto Saigo

摘要

This study tackles key challenges in parameter estimation for stochastic differential equations (SDEs) driven by non-Gaussian noise, which are crucial for modeling dynamic phenomena like price fluctuations and epidemic spread. Traditional quasi-likelihood methods struggle in complex SDE scenarios due to strong assumptions and step-size constraints. Recent data-driven approaches using neural networks have shown promise but face issues like performance degradation on long sequences and limited generalization at domain boundaries. We propose the Multi-level Parameter Estimation Network (MLPEnet), a three-stage model incorporating a parameter heterogeneity condensation phase to improve inference speed and generalization. Experimental results on synthetic datasets indicate that MLPEnet provides better overall accuracy compared to previous methods and effectively reduces performance decline at the boundaries of the training domain, highlighting its potential for broad applicability.