On Some Results of the Nonuniqueness of Solutions Obtained by the Feynman–Kac Formula-Reference-Cited by-同舟云学术

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

Published:2023-12-30 Issue:1 Volume:12 Page:129
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Choi Byoung Seon¹,Choi Moo Young²^ORCID

Affiliation:

1. Graduate School of Data Science, Department of Economics, Seoul National University, Seoul 08826, Republic of Korea

2. 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.

Funder

National Research Foundation of Korea

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/12/1/129/pdf

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4. On distributions of certain Wiener functionals;Kac;Trans. Am. Math. Soc.,1949

5. Neyman, J. (August, January 31). On some connections between probability theory and differential and integral equations. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA.