Diop (2026) A Unified Framework for Stochastic Differential Equations Driven by H ö lder Continuous Functions with Applications to Senegalese Groundwater Management

Identification

• Journal: American Journal of Applied Mathematics
• Year: 2026
• Authors: Bou Diop
• DOI: 10.11648/j.ajam.20261401.12

Research Groups

• Department of Mathematics, IBA DER THIAM University, Thiès, Senegal.

Short Summary

This research establishes a unified mathematical framework for stochastic differential equations (SDEs) driven by Hölder continuous paths, bridging Young integration and rough path theory. The application of this framework to Senegalese hydrology results in a 52% improvement in groundwater level prediction accuracy compared to traditional stochastic models.

Objective

• To develop a comprehensive theoretical and numerical framework for SDEs driven by irregular paths that establishes existence, uniqueness, and regularity across the entire Hölder roughness spectrum.

Study Configuration

• Spatial Scale: Regional (Senegal, specifically semi-arid groundwater systems).
• Temporal Scale: Not explicitly defined in the text, though focused on drought early warning and long-term sustainable water resource planning.

Methodology and Data

• Models used: Stochastic Differential Equations (SDEs), a novel Newton-Cotes integration method (bridging Young integration and rough path theory), and adaptive numerical schemes.
• Data sources: Irregular hydrological data patterns and time series related to Senegalese groundwater; parameter estimation utilized combined Maximum Likelihood and Bayesian approaches.

Main Results

• Established a novel Newton-Cotes integration method that provides solutions for processes with Hölder continuous sample paths.
• Developed adaptive numerical schemes with mathematically proven convergence rates.
• Demonstrated a 52% quantitative improvement in prediction accuracy for groundwater management in Senegal over traditional modeling methods.
• Improved the reliability of drought early warning systems and sustainable water resource planning in climate-uncertain semi-arid regions.

Contributions

• Introduces an innovative mathematical bridge between classical Young integration and modern rough path theory.
• Provides a unified theoretical foundation for SDEs that is applicable across the entire spectrum of path roughness.
• Demonstrates the practical scalability of advanced stochastic calculus from theoretical mathematics to real-world environmental engineering and resource management.

Funding

• Information regarding specific projects, programs, or reference codes was not provided in the source text.

Citation

@article{Diop2026Unified,
  author = {Diop, Bou},
  title = {A Unified Framework for Stochastic Differential Equations Driven by H ö lder Continuous Functions with Applications to Senegalese Groundwater Management},
  journal = {American Journal of Applied Mathematics},
  year = {2026},
  doi = {10.11648/j.ajam.20261401.12},
  url = {https://doi.org/10.11648/j.ajam.20261401.12}
}

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