Potential Analysis

, Volume 48, Issue 3, pp 257–300 | Cite as

An Integrated Version of Varadhan’s Asymptotics for Lower-Order Perturbations of Strong Local Dirichlet Forms

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Abstract

The studies of J. A. Ramírez, Hino–Ramírez, 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.

Keywords

Varadhan’s asymptotics Short-time behavior Dirichlet form Intrinsic distance 

Mathematics Subject Classification (2010)

31C25 60J60 58J37 47D07 

Notes

Acknowledgements

This study was supported by JSPS KAKENHI Grant Number JP15H03625.

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.Mathematical InstituteTohoku UniversityAobaJapan

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