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

被引：0

作者：

Choi, Byoung Seon ^{[1
]}

Choi, Moo Young ^{[2
]}

机构：

[1] Seoul Natl Univ, Grad Sch Data Sci, Dept Econ, Seoul 08826, South Korea

[2] Seoul Natl Univ, Ctr Theoret Phys, Dept Phys & Astron, Seoul 08826, South Korea

来源：

MATHEMATICS | 2024年 / 12卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Feynman-Kac formula; Schrodinger equation; partial differential equation; Brownian motion; uniqueness;

D O I：

10.3390/math12010129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Feynman-Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrodinger 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.

引用

页数：10

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