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On Some Results of the Nonuniqueness of Solutions Obtained by the Feynman–Kac Formula

Author

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  • Byoung Seon Choi

    (Graduate School of Data Science, Department of Economics, Seoul National University, Seoul 08826, Republic of Korea)

  • Moo Young Choi

    (Department of Physics and Astronomy, Center for Theoretical Physics, Seoul National University, Seoul 08826, Republic of Korea)

Abstract

The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics. Specifically, the formula provides a solution to the partial differential equation, expressed as an expectation value for Brownian motion. This paper demonstrates that the Feynman–Kac formula does not produce a unique solution but instead carries infinitely many solutions to the corresponding partial differential equation.

Suggested Citation

  • Byoung Seon Choi & Moo Young Choi, 2023. "On Some Results of the Nonuniqueness of Solutions Obtained by the Feynman–Kac Formula," Mathematics, MDPI, vol. 12(1), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:129-:d:1310819
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