Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 1, Pages 1-10
Some properties of the Feynman-Kac functional
1Matematisk Unstitut, Aarhus University, Aarhus, Denmark
2Department of Mathematics, University of Florida, Gainesville 32611, Florida, USA
Received 1 May 1994; Revised 1 December 1994
Copyright © 1995 S. Graversen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Feynman-Kac formula and its connections with classical analysis were
initiated in the now celebrated paper  of M. Kac. It soon became obvious that
the formula provides a powerful tool for solving partial differential equations by
running the Brownian motion process. K.L. Chung and K.M. Rao in  used it
to characterize solutions of the Schrödinger equation. In this paper we study
some properties of the Feynman-Kac functional using the Brownian motion process. In particular, we are going to use it in connection with the gauge function
in order to obtain an energy formula similar to one obtained by G. Dal Maso and
U. Mosco in .