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