A resolvent-type method for estimating time integrals of quadratic fluctuations in weakly asymmetric exclusion

TL;DR

This paper introduces a resolvent-type approach to estimate time integrals of quadratic fluctuations in weakly asymmetric exclusion processes, providing a new tool for analyzing such stochastic systems.

Contribution

It develops a resolvent-type method for estimating time integrals of functionals in right processes and applies it to weakly asymmetric exclusion, establishing a weak replacement lemma.

Findings

Established a resolvent-based estimation technique.

Proved a weak form of the replacement lemma.

Applied the method to weakly asymmetric exclusion processes.

Abstract

We describe a resolvent-type method for estimating time integrals of time-dependent functionals of general right processes in equilibrium and apply this result in the case of weakly asymmetric one-dimensional simple exclusion showing a weak form of a replacement lemma for quadratic fluctuations.