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Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise

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  • Wang, Xiaolong
  • Feng, Jing
  • Liu, Qi
  • Li, Yongge
  • Xu, Yong

Abstract

In this paper, a novel parameter estimation method based on a two-stage neural network (PENN) is proposed to carry out a joint estimation of a parameterized stochastic differential equation (SDE) driven by Lévy noise from a discretely sampled trajectory. The first stage is a long short term memory neural network to extract the compact time-irrelevant deep features from the trajectory. Then a fully connected neural network refines the deep features by integrating the information of time. This neural network architecture allows our method capable of processing trajectories with variable lengths and time spans. Representative SDEs including Ornstein–Uhlenbeck process, genetic toggle switch model and bistable Duffing system are presented to determine the effectiveness of our approach. The numerical results suggest that the PENN can simultaneously estimate the parameters of the system and Lévy noise with faster speed and higher accuracy in comparison with traditional estimation methods. Moreover, the method can be easily generalized to different SDEs with flexible settings of sample observation.

Suggested Citation

  • Wang, Xiaolong & Feng, Jing & Liu, Qi & Li, Yongge & Xu, Yong, 2022. "Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    • Handle: RePEc:eee:phsmap:v:606:y:2022:i:c:s0378437122007075
    DOI: 10.1016/j.physa.2022.128146
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    1. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    2. Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
    3. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    4. Long, Hongwei, 2009. "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2076-2085, October.
    5. Luis Valdivieso & Wim Schoutens & Francis Tuerlinckx, 2009. "Maximum likelihood estimation in processes of Ornstein-Uhlenbeck type," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 1-19, February.
    6. Wolfe, Stephen James, 1982. "On a continuous analogue of the stochastic difference equation Xn=[rho]Xn-1+Bn," Stochastic Processes and their Applications, Elsevier, vol. 12(3), pages 301-312, May.
    7. Betül Kalaycı & Ayşe Özmen & Gerhard-Wilhelm Weber, 2020. "Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS," Annals of Operations Research, Springer, vol. 295(1), pages 183-206, December.
    8. Thorsten Wagner & Alexandra Kroll & Chandrashekara R Haramagatti & Hans-Gerd Lipinski & Martin Wiemann, 2017. "Classification and Segmentation of Nanoparticle Diffusion Trajectories in Cellular Micro Environments," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-20, January.
    9. Feng, Jing & Xu, Wei & Xu, Yong & Wang, Xiaolong, 2018. "Phase transition and alternation in a model of perceptual bistability in the presence of Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 367-378.
    10. Hu, Yaozhong & Long, Hongwei, 2009. "Least squares estimator for Ornstein-Uhlenbeck processes driven by [alpha]-stable motions," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2465-2480, August.
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    1. Lee, Kyungsub, 2023. "Recurrent neural network based parameter estimation of Hawkes model on high-frequency financial data," Finance Research Letters, Elsevier, vol. 55(PA).
    2. Kyungsub Lee, 2023. "Recurrent neural network based parameter estimation of Hawkes model on high-frequency financial data," Papers 2304.11883, arXiv.org.
    3. Li, Shuaiyu & Wu, Yunpei & Cheng, Yuzhong, 2024. "Parameter estimation and random number generation for student Lévy processes," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).

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