Pathwise approximation of Feynman path integrals using simple random walks

TL;DR

This paper develops a rigorous mathematical framework for Feynman path integrals by employing strong, pathwise approximations using simple random walks, enhancing the theoretical understanding of quantum path integrals.

Contribution

It introduces a novel approach to approximate Feynman path integrals with simple random walks, providing a rigorous mathematical foundation.

Findings

Established convergence of random walk approximations to Feynman integrals

Provided explicit error bounds for the approximation

Enhanced the theoretical understanding of quantum path integrals

Abstract

The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.