Infinite dimensional integrals beyond Monte Carlo methods: yet another approach to normalized infinite dimensional integrals

TL;DR

The paper introduces a new Monte Carlo-inspired approach for computing normalized infinite-dimensional integrals, including oscillatory cases, by incorporating normalization directly into the evaluation process.

Contribution

It proposes a novel method for infinite-dimensional integrals that integrates normalization within the evaluation sequence, extending Monte Carlo techniques to more complex integrals.

Findings

Successfully recovers classical expectation values for cylinder functions

Handles normalized oscillatory integrals effectively

Provides a new framework for infinite-dimensional integral evaluation

Abstract

An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the normalization through the partition function is included in the definition. For suitable sequences of evaluations, the ("classical") expectation values of cylinder functions are recovered