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

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

Physica A: Statistical Mechanics and its Applications, 2022, vol. 606, issue C

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.

Keywords: Parameter estimation; Stochastic differential equation; Lévy noise; Neural network; Ornstein–Uhlenbeck process; Duffing system (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437122007075
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:606:y:2022:i:c:s0378437122007075

DOI: 10.1016/j.physa.2022.128146

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().