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

Byoung Seon Choi () and Moo Young Choi ()
Additional contact information
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

Mathematics, 2023, vol. 12, issue 1, 1-10

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.

Keywords: Feynman–Kac formula; Schrödinger equation; partial differential equation; Brownian motion; uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/1/129/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/1/129/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2023:i:1:p:129-:d:1310819

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().