An integrated version of Varadhan's asymptotics for lower-order perturbations of strong local Dirichlet forms

TL;DR

This paper extends Varadhan's asymptotics to non-symmetric bilinear forms combining strong local symmetric Dirichlet forms with lower-order perturbations, providing conditions for similar asymptotic behavior.

Contribution

It introduces sufficient conditions under which non-symmetric bilinear forms exhibit Varadhan-type asymptotics, broadening the scope of previous symmetric results.

Findings

Established asymptotics for non-symmetric forms with perturbations

Identified conditions ensuring Varadhan's asymptotics hold

Extended previous symmetric form results to more general cases

Abstract

The studies of Ram\'irez, Hino-Ram\'irez, and Ariyoshi-Hino showed that an integrated version of Varadhan's asymptotics holds for Markovian semigroups associated with arbitrary strong local symmetric Dirichlet forms. In this paper, we consider non-symmetric bilinear forms that are the sum of strong local symmetric Dirichlet forms and lower-order perturbed terms. We give sufficient conditions for the associated semigroups to have asymptotics of the same type.