Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 1, Pages 1-10
doi:10.1155/S1048953395000013

Some properties of the Feynman-Kac functional

S. Graversen,1 Z. R. Pop-Stojanović,2 and K. Murali Rao2

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 Hindawi Publishing Corporation. 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.

Abstract

The Feynman-Kac formula and its connections with classical analysis were initiated in the now celebrated paper [6] 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 [4] 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 [5].