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

Potential Analysis volume 48, pages257–300(2018)Cite this article

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.

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Acknowledgements

This study was supported by JSPS KAKENHI Grant Number JP15H03625.

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Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606–8502, Japan

    Masanori Hino

  2. Mathematical Institute, Tohoku University, Aoba, Sendai, 980–8578, Japan

    Kouhei Matsuura

Authors
  1. Masanori Hino
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  2. Kouhei Matsuura
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Corresponding author

Correspondence to Masanori Hino.

Additional information

Dedicated to Professor Masayoshi Takeda on the occasion of his 60th birthday

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Hino, M., Matsuura, K. An Integrated Version of Varadhan’s Asymptotics for Lower-Order Perturbations of Strong Local Dirichlet Forms. Potential Anal 48, 257–300 (2018). https://doi.org/10.1007/s11118-017-9634-x

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Keywords

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

Mathematics Subject Classification (2010)

  • 31C25
  • 60J60
  • 58J37
  • 47D07