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