The Partial Averaging method

TL;DR

The paper introduces and analyzes the partial averaging technique used with the Feynman-Kac formula, demonstrating its convergence properties for a broad class of potentials, including those with singularities.

Contribution

It provides a detailed mathematical analysis of the partial averaging method, establishing its convergence for Kato-class potentials with finite Gaussian transforms.

Findings

Converges for all Kato-class potentials with finite Gaussian transform

Enjoys good rates of convergence

Applicable to potentials with Coulombic singularities

Abstract

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.