Journal of the Mathematical Society of Japan

On divergence of expectations of the Feynman–Kac type with singular potentials

Yuu HARIYA and Kaname HASEGAWA

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Abstract

Motivated by the work of Baras–Goldstein (1984), we discuss when expectations of the Feynman–Kac type with singular potentials are divergent. Underlying processes are Brownian motion and $\alpha$-stable process. In connection with the work of Ishige–Ishiwata (2012) concerned with the heat equation in the half-space with a singular potential on the boundary, we also discuss the same problem in the half-space for the case of Brownian motion.

Article information

Source
J. Math. Soc. Japan Volume 68, Number 3 (2016), 1271-1296.

Dates
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1468956168

Digital Object Identifier
doi:10.2969/jmsj/06831271

Mathematical Reviews number (MathSciNet)
MR3523547

Zentralblatt MATH identifier
06642413

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60G52: Stable processes 35K05: Heat equation 60J55: Local time and additive functionals

Keywords
Feynman–Kac formula heat equation singular potential fractional Laplacian

Citation

HARIYA, Yuu; HASEGAWA, Kaname. On divergence of expectations of the Feynman–Kac type with singular potentials. J. Math. Soc. Japan 68 (2016), no. 3, 1271--1296. doi:10.2969/jmsj/06831271. https://projecteuclid.org/euclid.jmsj/1468956168.


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