Discrete approximation of symmetric jump processes on metric measure spaces

Zhen Qing Chen; Panki Kim; Takashi Kumagai

doi:10.1007/s00440-012-0411-x

Discrete approximation of symmetric jump processes on metric measure spaces

Zhen Qing Chen, Panki Kim^*, Takashi Kumagai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

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.

Original language	English
Pages (from-to)	703-749
Number of pages	47
Journal	Probability Theory and Related Fields
Volume	155
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-012-0411-x
Publication status	Published - 2013 Apr
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-012-0411-x

Cite this

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title = "Discrete approximation of symmetric jump processes on metric measure spaces",

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.",

keywords = "Dirichlet form, Jump process, Mosco convergence, Random conductance, Skorohod space, Symmetric jump process, Tightness, Weak convergence",

author = "Chen, {Zhen Qing} and Panki Kim and Takashi Kumagai",

note = "Funding Information: Takashi Kumagai{\textquoteright}s research partially supported by the Grant-in-Aid for Scientific Research (B) 22340017. Funding Information: Panki Kim{\textquoteright}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). Funding Information: Zhen-Qing Chen{\textquoteright}s research partially supported by NSF Grants DMS-0906743 and DMR-1035196. ",

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doi = "10.1007/s00440-012-0411-x",

language = "English",

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AU - Chen, Zhen Qing

AU - Kim, Panki

AU - Kumagai, Takashi

N1 - Funding Information: Takashi Kumagai’s research partially supported by the Grant-in-Aid for Scientific Research (B) 22340017. Funding Information: 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). Funding Information: Zhen-Qing Chen’s research partially supported by NSF Grants DMS-0906743 and DMR-1035196.

PY - 2013/4

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N2 - 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.

AB - 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.

KW - Dirichlet form

KW - Jump process

KW - Mosco convergence

KW - Random conductance

KW - Skorohod space

KW - Symmetric jump process

KW - Tightness

KW - Weak convergence

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JF - Probability Theory and Related Fields

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Discrete approximation of symmetric jump processes on metric measure spaces

Abstract

Keywords

ASJC Scopus subject areas

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