The Partial Averaging method

The partial averaging technique is defined and used in conjunction with the random series implementation of the Feynman-Kac formula. It enjoys certain properties such as good rates of convergence and convergence for potentials with coulombic singularities. In this work, I introduce the reader to the technique and I analyze the basic mathematical properties of the method. I show that the method is convergent for all Kato-class potentials that have finite Gaussian transform.