Author(s)

Yidan Feng ¹

Affiliation(s)

¹ College of Science, Northeastern University, Boston, 02120, USA

Corresponding Author

Yidan Feng

ABSTRACT

This research paper introduces a new computational scheme that uses regression techniques to solve high-dimensional partial differential equations (PDEs) through the Feynman-Kac formula and Monte Carlo Method (MCM) simulations. The conventional approach using interpolation faces significant challenges in high-dimensional spaces, which will cause more complex computations and less accuracy. The proposed method integrates stochastic differential equations (SDEs) and regression analysis to formulate a more efficient and accurate algorithm for computing global solutions. Comparing the traditional interpolation method with the new regression-based approach demonstrates significant improvements in computational efficiency and a reduction in error. The paper meticulously analyzes the error differences, convergence properties, and the practical implications of the regression method in overcoming the limitations faced by interpolation in high-dimensional problem spaces. The results underscore the potential of this new scheme to enhance the accuracy and speed of solving PDEs using the Feynman-Kac and MCM, offering a substantial contribution to the field of numerical analysis and computational mathematics.

KEYWORDS

Partial differential equation, Feynman-Kac formula, Brownian Motion, regression

CITE THIS PAPER

Yidan Feng, Optimum Scheme of Feynman-Kac Formula Based on Regression and Monte Carlo Methods. Transactions on Computational and Applied Mathematics (2024) Vol. 4: 104-112. DOI: http://dx.doi.org/10.23977/tracam.2024.040114.

REFERENCES

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