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Discrete approximation of symmetric jump processes on metric measure spaces
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  • Published: 28 January 2012

Discrete approximation of symmetric jump processes on metric measure spaces

  • Zhen-Qing Chen1,
  • Panki Kim2 &
  • Takashi Kumagai3 

Probability Theory and Related Fields volume 155, pages 703–749 (2013)Cite this article

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Abstract

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a large class of symmetric jump processes. We also discuss some application of our results to the scaling limit of random walk in random conductance.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen

  2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul, 151-747, Republic of Korea

    Panki Kim

  3. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Takashi Kumagai

Authors
  1. Zhen-Qing Chen
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  2. Panki Kim
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  3. Takashi Kumagai
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Corresponding author

Correspondence to Panki Kim.

Additional information

Zhen-Qing Chen’s research partially supported by NSF Grants DMS-0906743 and DMR-1035196.

Panki Kim’s research supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (0409-20110087).

Takashi Kumagai’s research partially supported by the Grant-in-Aid for Scientific Research (B) 22340017.

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Cite this article

Chen, ZQ., Kim, P. & Kumagai, T. Discrete approximation of symmetric jump processes on metric measure spaces. Probab. Theory Relat. Fields 155, 703–749 (2013). https://doi.org/10.1007/s00440-012-0411-x

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  • Received: 31 August 2010

  • Revised: 25 December 2011

  • Published: 28 January 2012

  • Issue Date: April 2013

  • DOI: https://doi.org/10.1007/s00440-012-0411-x

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Keywords

  • Weak convergence
  • Mosco convergence
  • Tightness
  • Skorohod space
  • Dirichlet form
  • Random conductance
  • Jump process
  • Symmetric jump process

Mathematics Subject Classification (2000)

  • Primary 60B10
  • 60J25
  • Secondary 60J35
  • 60G52
  • 60J75
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