Deep Learning for solving Fokker-Planck-Kolmogorov  
Equation Arising from Jump-Diffusion Model

Xingyu Zhang; Jianguo Tan

doi:https://doi.org/10.14445/22315373/IJMTT-V71I2P101

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 2 | Year 2025 | Article Id. IJMTT-V71I2P101 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I2P101

Deep Learning for solving Fokker-Planck-Kolmogorov Equation Arising from Jump-Diffusion Model

Xingyu Zhang, Jianguo Tan

Received	Revised	Accepted	Published
17 Dec 2024	20 Jan 2025	04 Feb 2025	18 Feb 2025

Abstract

The Fokker-Planck-Kolmogorov (FPK) equation generated by the jump-diffusion model is represented as a Partial Integro-Differential Equation (PIDE). Traditional numerical methods for solving PIDEs are often constrained by dimensionality and the complexity of mesh generation. To address these limitations, this paper proposes a novel deep-learning approach for solving PIDEs. Building upon the existing Physics-Informed Neural Network (PINN) framework for solving Partial Differential Equations (PDEs), we incorporate additional deep neural networks (DNNs) and construct a novel loss function to simultaneously optimize the integral terms and the solution for approximating the PIDE. The results demonstrate that our approach accurately captures the system's dynamic behaviour, highlighting its effectiveness and potential for solving complex PIDEs.

Keywords

Deep learning, Partial integro-differential equation, Jump-diffusion model, Fokker-Planck-Kolmogorov equation, Gaussian and Poisson white noises.

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Citation :

Xingyu Zhang, Jianguo Tan, "Deep Learning for solving Fokker-Planck-Kolmogorov Equation Arising from Jump-Diffusion Model," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 2, pp. 1-6, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I2P101