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

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

doi:10.1016/j.physa.2022.128146

Cited by 15 publications

(2 citation statements)

References 41 publications

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“…In alignment with methodologies outlined in [20], [21] and [27], we make the assumption that the population, denoted as y t at time t, follows a stochastic model, represented as:…”

Section: Derivation Of Stochastic Growth Modelmentioning

confidence: 99%

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Chidzalo,

Abonongo,

Naryongo

2023

Computational Journal of Mathematical and Statistical Sciences

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Growth models play a pivotal role in diverse fields, such as population dynamics, epidemiology, finance, and ecological systems. Traditionally, deterministic growth models have been extensively employed to capture various aspects of growth phenomena. However, in real-world scenarios, stochasticity is inherent in the data, challenging the suitability of deterministic models. Consequently, there is a growing interest in developing stochastic growth models capable of accommodating inherent uncertainties. This study addresses three fundamental questions within the context of stochastic growth modeling. Firstly, it investigates the continued reliability of the Method of Three Selected Points (MTSP) for estimating parameters in stochastic differential equations (SDEs), given the increasing popularity of stochastic models over deterministic ones. Secondly, it explores the required form of SDEs that maximizes the success and reliability of the MTSP approach. Lastly, it conducts a comparative analysis of the MTSP method against commonly employed techniques in the literature. To address these questions, we propose a novel approach to constructing SDEs that enhance the stability of both bounded and unbounded stochastic growth models. By carefully selecting the form of the diffusion coefficient, we achieve higher accuracy in estimating the parameters of the drift coefficient. Through empirical simulations and a comprehensive reliability analysis using real stock data, we demonstrate the superior performance of the MTSP method when compared to the Pseudo-maximum likelihood method and physics-informed neural networks within the framework of SDEs. Our findings underscore the continued effectiveness of the MTSP method for estimating parameters in stochastic growth models, even in an era where stochastic models dominate. Additionally, we provide insights into the optimal structure of SDEs for maximizing the reliability of the MTSP approach. Thus, the study contributes to the ongoing dialogue surrounding stochastic growth modeling and offers a robust methodology for parameter estimation in this context, with practical applications in fields ranging from epidemiology to finance.

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“…In alignment with methodologies outlined in [20], [21] and [27], we make the assumption that the population, denoted as y t at time t, follows a stochastic model, represented as:…”

Section: Derivation Of Stochastic Growth Modelmentioning

confidence: 99%

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Chidzalo,

Abonongo,

Naryongo

2023

Computational Journal of Mathematical and Statistical Sciences

View full text Add to dashboard Cite

show abstract

“…Thus, we consider the nonparametric neural network estimator (Suzuki 2018;Oono and Suzuki 2019;Schmidt-Hieber 2020) as our ansatz function class, which has achieved great success in estimating SDE coefficients empirically (Xie et al 2007;Zhang et al 2018;Han, Jentzen, and E 2018;Wang et al 2022;Lin, Li, and Ren 2023). We aim to build statistical guarantees for such neural network-based estimators.…”

Section: Introductionmentioning

confidence: 99%

Statistical Spatially Inhomogeneous Diffusion Inference

Ren,

Lu,

Ying

et al. 2024

AAAI

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Inferring a diffusion equation from discretely observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments. Assuming that the underlying dynamical process obeys a d-dimensional stochastic differential equation of the form dx_t = b(x_t)dt + \Sigma(x_t)dw_t, we propose neural network-based estimators of both the drift b and the spatially-inhomogeneous diffusion tensor D = \Sigma\Sigma^T/2 and provide statistical convergence guarantees when b and D are s-Hölder continuous. Notably, our bound aligns with the minimax optimal rate N^{-\frac{2s}{2s+d}} for nonparametric function estimation even in the presence of correlation within observational data, which necessitates careful handling when establishing fast-rate generalization bounds. Our theoretical results are bolstered by numerical experiments demonstrating accurate inference of spatially-inhomogeneous diffusion tensors.

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提取受非高斯列维噪声扰动随机动力系统的最大似然转移路径的数据驱动方法

Lu,

Li,

Liu

2023

Acta Mech. Sin.

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

Cited by 15 publications

References 41 publications

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Statistical Spatially Inhomogeneous Diffusion Inference

提取受非高斯列维噪声扰动随机动力系统的最大似然转移路径的数据驱动方法

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

Cited by 15 publications

References 41 publications

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Statistical Spatially Inhomogeneous Diffusion Inference

提取受非高斯列维噪声扰动随机动力系统的最大似然转移路径 的数据驱动方法

Contact Info

Product

Resources

About

提取受非高斯列维噪声扰动随机动力系统的最大似然转移路径的数据驱动方法